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26 Cards in this Set

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____ ____ ____ (lambda) - change in population size over a specific time interval (eg. 1 year)
finite growth rate

best for individuals that don't reproduce continuously (distinct "breeding" season)

called "geometric growth" or "discrete growth"
_____ ____ ____ - theoretical rate of change as the "time step" becomes smaller and smaller, approaching zero
instantaneous growth rate

appropriate for continuously reproducing populations (bacteria, some tropical insects, humans)

called "exponential growth" or "continuous growth"
equation for geometric growth
Nt = N0 * lambda(t)
equation for exponential growth
Nt = N0 * e^rt
r
per capita growth rate

r = b - d
computational form of r formula
r = [ln(Nt) - ln(N0)] / t
lambda = 1
r = 0
population size is constant
lambda > 1
r > 0
population is growing
lambda < 1
r < 0
population is declining
conversion of lambda to r
r = ln(lambda)
equation for finding doubling time in an exponentially growing population
rt = 0.693
continuous reproduction
stable age distribution
constant "b" and 'd' (constant 'r')
implies constant environment and unlimited resources
assumptions for exponential growth model
when are exponential growth requirements met in nature?
introduction of species into new habitat (zebra mussel)
population recovering from disturbance
modern humans
Thomas Malthus came up with these ideas in an essay on the principle of population in 1798
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
describes a population limited by resources
logistic population growth
equation for logistic population growth model
dN/dt = r max(N) * [(K-N)/K]

rate of population increase = max possible rate * proportion of resources available
the realized growth rate of the population (dN/dt) depends on the ____ ____
population size

example of density-dependent population regulation
density-dependent regulation requires...
-- birth rates (b) that ____ w/ increasing N and/or...
-- death rates (d) that _____ w/ increasing N
decrease
increase
what happens if b or d are non-linear functions of N?
can have stable and unstable equilibrium points

unstable equilibrium point = "critical minimum N"
population growth rates decline if N drops below a minimum critical value
Allee effect
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
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
growth rate has slowed recently, to about ____% per year
1.21%

if this rate is maintained, there would be roughly 16 billion ppl on earth in 2080
current population size
about 7 billion
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
in net reproductive rate went to r0 = 1 right now, would the population stop growing tomorrow?
NO

it would take several decades (probably a few generations) for the population age structure and growth rate to stabilize