Flashcards in Chapter 12 Lecture 3 Deck (38)

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1

## how do populations often grow

### exponentially

2

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

### the death rates+ emigration

3

## what serves to regulate population growth

### any factor that slows down the inputs relative to the outputs

4

## factors that slow down the inputs relative to the outputs

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

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"

### 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

6

## 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).

7

## 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

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:

###
dn/dt = rN

r = r0(1 - N/K)

9

## r0

### intrinsic rate of growth when its size is close to 0

10

## K

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

11

## r=

###
r0(1 - N/K)

or

r0 - r0N/K

12

## r = r0 - r0N/K

### defines a straight line with slope -r0/K

13

## y

### dependent

14

## x

### independent

15

## m

### slope

16

## b

### y intercept

17

## N

### independent variable

18

## r

### dependent variable

19

## slope

### -r0/K

20

## logistic equation (equation for restrained growth

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

21

## what shape is the logistic curve

### hump-shaped

22

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

###
(dN/dt) = 0

(when N = 0 and when K = N)

23

## when does the peak of the hump occur

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

24

## Carrying capacity (K):

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

25

## Logistic growth model

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

26

## what is the logistic growth model represented by

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

27

## S-shaped curve

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

28

## Inflection point

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

29

## early growth is

### exponential

30