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Principles of Eco Chapt 10-11 Exam2

front 1

Population Size equation

back 1

Nt+1 = Nt + B - D

t+1= pop size at the end of time

t = pop size at the beginning of time

front 2

With a constant 10% annual rate of increase:

back 2

A population of 100 will add 10 individuals per year.
• A population of 1000 will add 100 individuals per year.
• A population of 10 billion adds 1 billion individuals per year.

constant rate would rapidly climb toward infinity

front 3

Geometric growth happens during a single time period uses the equation

back 3

N(t+1)=N(t) λ

N(t + 1) = number of individuals at end of period
N(t) = number of individuals at start of period
lambda(λ) = geometric population growth rate
(the multiple by which the population grows in each time period)

front 4

Geometric Growth happens during multiple periods, uses the equation

Fig 11.4 (has both expontential and logistic growth)

back 4

Nt = N0 λ t

Nt = # individuals after t units of time
N0 = initial population size at time(0)
lambda(λ) = geometric population growth rate (the multiple by which the population grows in each time period)
t = number of time periods (hours, days, years, etc)

GO OVER EXAMPLES ON SLIDES 24

front 5

Expotentionel pop growth equation

back 5

Nt = N0 ert

Nt = number of individuals after t time units
N0 = initial population size at time(0)
r = exponential growth rate per unit time (or intrinsic rate of increase)
e = base of the natural logarithms (about 2.72)
t = number of units of time

front 6

Rate of increase in pop size equation

back 6

dN/dt = rN

(r) expresses population increase on a “per capita” or “per individual” basis.
• The instantaneous increase/decrease in population size per unit time (dN/dt) varies in direct proportion to N (the current
population size).

front 7

Geometric and exponetial growth patterns overlap equation

back 7

λ = er

front 8

Per capita exponential growth rate equation:

back 8

r=b-d

If birth rate is higher than death rate, then r is positive.
If death rate is higher than birth rate, then r is negative.

front 9

Growth rates whether the pop size increases, decreases or stays the same

back 9

You have a continuously
decelerating curve of
decrease when r < 0

You have a continuously
accelerating curve of
increase when r > 0.

front 10

Density-independent factors affect population size and

back 10

per capita growth rate

Ex. abiotic factors such as weather,
climate, and natural disasters

Fig 11.8 (highest year 1939 for thrips)

front 11

Density Dependent factors affect pop size and

back 11

growth rate as a consequence of pop density

Ex. food availability, habitat availability, predation rates, and parasite infection loads

Basically, when pop is large and food is scare, death is on the rise and birth rates decrease (Fig 11.11)

front 12

Density dependent reproduction and death rates can regulate pop size but

back 12

at high densities, pop growth may decline

Fig 11.12 (Pop growth rates declining)

front 13

The types of limits to exponential and geometric pop growth are

back 13

Populations exhibit geometric and exponential growth when resources are abundant. However, since resources eventually become limited, this growth cannot continue indefinitely.
Concept 11.3, Objective 1, Slide 43

front 14

Proposal of Pearl and Reed to changing exponential growth equation to logistic growth equation is

back 14

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

r0 = maximum exponential growth rate
N = actual population size
K = carrying capacity, or the maximum N supportable by the
resources in the environment.

front 15

This means population size always converges on equilibrium carrying
capacity (K):

read slides 48-55

back 15

populations below K grow
• populations above K decrease
• a population at K remains constant

front 16

Birth rates tend to decline in countries where income increases.
With rising income,

back 16

children are increasingly perceived as a
liability rather than an asset.

front 17

Population projections vary greatly, the median scenario predicting a plateau at

back 17

10.4 billion in 2050

front 18

When each new cohort is larger than the last, the pop is

When each new cohort is
smaller than the last, the pop is

back 18

growing

declining

Fig 11.16

front 19

In Fig 11.17, which survorship curive best describes humans?

back 19

Type 1 where most individuals survive to old age

Type 2 Straight line down (die at any age)

Type 3 Individuals die young