Chapter 12 Lecture 3

Question 1

how do populations often grow

Answer 1

exponentially

Question 2

for population growth, birth rates + immigration must be > than

Answer 2

the death rates+ emigration

Question 3

what serves to regulate population growth

Answer 3

any factor that slows down the inputs relative to the outputs

Question 4

factors that slow down the inputs relative to the outputs

Answer 4

predation, competition for scarce resources, herbivory, parasitism, disease, severe winter, drought

Question 5

Raymond Pearl and L.J. Reed “On the Rate of Growth of the Population of the United States since 1790 and its Mathematical Representation”

Answer 5

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

Question 6

what did pearl and reed also reason

Answer 6

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).

Question 7

what did pearl and reed suggest

Answer 7

rather than using a
constant value for r which really represents unrestrained
population growth —- r should decrease as N increases

Question 8

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:

Answer 8

dn/dt = rN
r = r0(1 - N/K)

Question 9

r0

Answer 9

intrinsic rate of growth when its size is close to 0

Question 10

K

Answer 10

carrying capacity of the environment, the max number of individuals that the environment can sustain indefinitely

Question 11

r=

Answer 11

r0(1 - N/K)
or
r0 - r0N/K

Question 12

r = r0 - r0N/K

Answer 12

defines a straight line with slope -r0/K

Question 13

y

Answer 13

dependent

Question 14

x

Answer 14

independent

Question 15

m

Answer 15

slope

Question 16

b

Answer 16

y intercept

Question 17

N

Answer 17

independent variable

Question 18

r

Answer 18

dependent variable

Question 19

slope

Answer 19

-r0/K

Question 20

logistic equation (equation for restrained growth

Answer 20

dN/dt = r0N(1 - N/K)

Question 21

what shape is the logistic curve

Answer 21

hump-shaped

Question 22

what is the rate of growth of the logistic curve at two population densities

Answer 22

(dN/dt) = 0

when N = 0 and when K = N

Question 23

when does the peak of the hump occur

Answer 23

N = K/2 (1/2 to carrying capacity)

Question 24

Carrying capacity (K):

Answer 24

the maximum population size that can be supported by the environment.

Question 25

Logistic growth model

Answer 25

a growth model that describes slowing growth of populations at high densities

Question 26

what is the logistic growth model represented by

Answer 26

dN/dt = rN(1-N/K)

Question 27

S-shaped curve

Answer 27

the shape of the curve when a population is graphed over time using the logistic growth model

Question 28

Inflection point

Answer 28

the point on a sigmoidal growth curve at which the population has its highest growth rate

Question 29

early growth is

Answer 29

exponential

Question 30

inflection point

Answer 30

the point of the fastest growth after which growth begins to slow

Question 31

As the population increases from a very small size, what happens to the rate of increase?

Answer 31

it grows until reaching 1/2 the carrying capacity (corresponding to the inflection point)

Question 32

Rate of per capita increase can be modeled as:

Answer 32

(1/N)(dN/dt)

Question 33

Individuals in the population continually decline in

Answer 33

their ability to contribute to population growth

Question 34

where does maximum growth occur

Answer 34

N = K/2

Question 35

as long as population size N doesn’t exceed the carrying capacity (N/K < 1), the population

Answer 35

continues to increase

Question 36

when the value of N exceeds the value of K, the ratio N/K

Answer 36

exceeds 1 and population growth declines

Question 37

the carrying capacity of a population is the eventual theoretical equilibrium size of

Answer 37

a population growing according to the logistic equation

Question 38

When examining population growth over a period of time (the time course of population growth)…

Answer 38

a sigmoid or S-shaped curve is formed on the X axis over time