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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) * [(KN)/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 densitydependent population regulation 

densitydependent 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 nonlinear 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 densitydependent 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 