Chapter 12 Lecture 3 Flashcards
how do populations often grow
exponentially
for population growth, birth rates + immigration must be > than
the death rates+ emigration
what serves to regulate population growth
any factor that slows down the inputs relative to the outputs
factors that slow down the inputs relative to the outputs
predation, competition for scarce resources, herbivory, parasitism, disease, severe winter, drought
Raymond Pearl and L.J. Reed “On the Rate of Growth of the Population of the United States since 1790 and its Mathematical Representation”
Pop. growth in the U.S. declined - if the decline followed a regular pattern, it should be able to be described with a mathematical formula, and future population growth could be predicted
what did pearl and reed also reason
the rate of exponential
growth in the population would be related to population
size rather than time alone (since any time scale for any
population is arbitrary).
what did pearl and reed suggest
rather than using a
constant value for r which really represents unrestrained
population growth —- r should decrease as N increases
rather than using a
constant value for r which really represents unrestrained
population growth —- r should decrease as N increases according to the following relation:
dn/dt = rN r = r0(1 - N/K)
r0
intrinsic rate of growth when its size is close to 0
K
carrying capacity of the environment, the max number of individuals that the environment can sustain indefinitely
r=
r0(1 - N/K)
or
r0 - r0N/K
r = r0 - r0N/K
defines a straight line with slope -r0/K
y
dependent
x
independent
m
slope