Chapter 12 Lecture 3 Flashcards

1
Q

how do populations often grow

A

exponentially

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2
Q

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

A

the death rates+ emigration

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3
Q

what serves to regulate population growth

A

any factor that slows down the inputs relative to the outputs

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4
Q

factors that slow down the inputs relative to the outputs

A

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

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5
Q

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

A

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

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6
Q

what did pearl and reed also reason

A

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).

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7
Q

what did pearl and reed suggest

A

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

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8
Q

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:

A
dn/dt = rN
r = r0(1 - N/K)
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9
Q

r0

A

intrinsic rate of growth when its size is close to 0

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10
Q

K

A

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

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11
Q

r=

A

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

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12
Q

r = r0 - r0N/K

A

defines a straight line with slope -r0/K

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13
Q

y

A

dependent

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14
Q

x

A

independent

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15
Q

m

A

slope

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16
Q

b

A

y intercept

17
Q

N

A

independent variable

18
Q

r

A

dependent variable

19
Q

slope

A

-r0/K

20
Q

logistic equation (equation for restrained growth

A

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

21
Q

what shape is the logistic curve

A

hump-shaped

22
Q

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

A

(dN/dt) = 0

when N = 0 and when K = N

23
Q

when does the peak of the hump occur

A

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

24
Q

Carrying capacity (K):

A

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

25
Q

Logistic growth model

A

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

26
Q

what is the logistic growth model represented by

A

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

27
Q

S-shaped curve

A

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

28
Q

Inflection point

A

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

29
Q

early growth is

A

exponential

30
Q

inflection point

A

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

31
Q

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

A

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

32
Q

Rate of per capita increase can be modeled as:

A

(1/N)(dN/dt)

33
Q

Individuals in the population continually decline in

A

their ability to contribute to population growth

34
Q

where does maximum growth occur

A

N = K/2

35
Q

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

A

continues to increase

36
Q

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

A

exceeds 1 and population growth declines

37
Q

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

A

a population growing according to the logistic equation

38
Q

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

A

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