Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
26 Cards in this Set
- Front
- Back
____ ____ ____ (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 |