# POPULATION GROWTH and MEASUREMENT

```POPULATION GROWTH &
MEASUREMENT
AP Environmental Science
Chapter 6
WHAT IS A POPULATION?
POPULATION SIZE is
A group of
determined by:
interbreeding
individuals within
a. #of births (based
a geographical
on fertility rates)
location.
b. # of deaths
c. # of indiv that
enter or leave the
population
Population Graphs measure
status of populations
J-curve or
Exponential
Growth
Curve
S-Curve or
Logistics
Curve
POPULATION DENSITY
DENSITY: number of
individuals per unit area
or volume
Ex: Suppose there are
150 bullfrogs living in a
pond that covers an
area 3 square km.
What is the population
density?
Population density
Population Density =
Number of Individuals (150 frogs)
Unit Area
(3 sq KM)
= 50 bullfrogs per square kilometer!
Populations Dynamics
 Population Modeling
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CARRYING CAPACITY
Max population
that a habitat
can support
(Level line)
D
I
S
E
A
S
E
D
I
S
A
s
T
E
R
S
=
P
R
E
D
A
T
O
R
S
F
O
O
D
Carrying Capacity Factors
These limiting pressures keep a
population in check such as carrying
capacity:




1. # of Predators
2. Amount of Food & Water Resources
Disease
Natural Disasters
 Reproductive ability
Other factors – H I P P O can
decrease in population!!





H=Habitat
I= Invasive species
P= Pollution
P=Other interacting populations
O=Overconsumption
Exponential Increase (J-curve)
In a J-curve,
the popul keeps
growing
quickly
(exponentially
over time).
What causes J-curve to occur?
Conditions:
1. No enemies
2. No competition.
3. Plenty of food & water
4. Low % of disease
J-curve is usually a temporary
situation=Population crash.
Exponential Growth Math Model
Change in N
Initial Population
Change in time
Rate of reproduction
Time
dN/dt = rN
Time
(dt)
N
(dN)
Rate
(r)*
rxN
Exponentially
how does it look
for a
J-curve
T1
2
10
10x2 = 20
2x10
T2
20
10
10x20=200
2x10x10
T3
200
10
10x200=2,000
2x10x10x10
T3
2000
10
10x2,000=20,000
2x10x10x10x10
T4
20,000 10
10x20,000=200,000 2x10x10x10x10x10
N=2 cockroaches (male and female)
r= 2 cockroaches can produce 20 offspring in 3 months
a. The rate of growth (r) 20/2 adults or 10 per 1 adult.
b. The growth rate (r) equals 10
Figure 06_03
Exponential Growth can Crash
 When population
can no longer
sustain itself
without food
resources, pop
decrease beneath
the carrying
capacity.
Population Crash
Isle Royale, Michigan
National Park
Moose pop
quickly in 1991-1995.
Wolf pop
due to
Parvovirus passed on
from domesticated dogs
visiting the National
Park.
Moose population
Due to tick infestation.
S-curve (Logistics curve)
S-curve or Logistics Population
1. Population at equilibrium.
2. S-curve may change (increase &
decrease) slightly, but is constant
near the carrying capacity.
3. May be considered “restricted
growth”.
Factors that keep populations
within carrying capacity
Migration
Logistics Curve Model
 dN =
dt
rN 1-N
K
dN = change of population over time
dt
N = Population
K= Current Carrying Capacity
r= rate of change or reproductive rate of a speciesd
Logisitics/Carrying Capacity
Connection
If the carrying capacity (K) = 100
wolves
If the N = 100 wolves (wolves bred
successfully to increase population)
Look at the 1-N/K part: 1 - 100
100
1- 1 = 0
dN/dt = rN(0)=0!!!
Logistics & CC (continued)
There is no change in dN/dt-no
population growth!
What if N=50? Plug it into 1-N/K to see
how it affects the reproductive rate for a
population.
1-50/100 = 1-1/2 = 1/2rN or half of the
maximum reproductive rate for the
wolves.
Logistics & CC (continued)
 If N = 10…plug into 1-N/K
(1- 10) = (1-.10) = .90
100
dN = rN(.90) or dN is
at a rate of
dt
dt
90% as fast as the max possible
reproductive rate for the wolves!
Lincoln Peterson Population
Estimate Model
Estimating population size by random
sampling an ecosystem.
Focus on population density or animal
abundance.
Est Population
Model: n1 = m2 OR N= n1 x n2
N
n2
m2
n1=#animal marked & released 1st time
n2=# animals captured during 2nd session
m2-# animals captured during 2nd session & are marked.
Population Measurement
in Review
J-curve
•Exponential Curve
S-curve
•Logistics Curve
•Carrying Capacity
Population Equilibrium
Equilibrium: the balance between births
and deaths within a population
Other Population Considerations
Environmental
Resistance
Population
Dispersal
Reproductive
Potential
Environmental Resistance
Factors/pressures that limit a
population’s ability to increase (CC)
Density Dependent
Density Independent
Parasites
Temperature
Disease
Moisture, light, pH salinity
Competitors
Weather
Predators
Natural Disasters
Human Intervention
Lack of habitat/territory
Population Dispersal
Definition
Different patterns of how a species or
population will inhabit a certain
geographical location.
Population Dispersal is
determined by:
Population
Dispersal
Uniform
Clumped
Random
POPULATION DISPERSAL
A. RANDOM:
1. Least Common
2. Found anywhere in
envir.
3. High mobility such
as wind blown
Ex: Dandelions
POP DISPERSAL
B. Uniform
1. Rare Occurrence but does occur
in nature! (Hawks, wolves)
2. Can indicate human impact
a. Plantations, orchards, etc.
UNIFORM POPULATION DISP.
Red-Tailed Hawk
Orchards
CLUMPED POP DISPERSAL
C. CLUMPED:
1. Patchy, most
common
2. Protection, avail of
natural resources,
to survive
3. Ex: Allelopathy,
fish, plants, trees,
etc.
Clumped Dispersal – Purple
Loosestrife Patterns in US
Reproductive Potential
…Is an organism’s
ability to grow at the
fastest rate.
(To replenish the
species—innate!)
REPRODUCTIVE
POTENTIAL COMPARISON
1. R-selected
Hint: Rapid Repro
2. K-selected
Hint: Longer Repro
a.
b.
c.
d.
a.
b.
c.
d.
e.
Early reproduction
Short life span
Hi mortality
Little/no parental
care
e. Large # of offspring
produced
f. Inhabit lower trophic
levels (1st order
consumers)
Late reproduction
Long life span
Low mortality
High parental care
Small # of offspring
produced
REPRODUCTION TYPES
K-SELECTED TYPE
R-SELECTED
TYPES
Reproductive potential – “R”
Bacterium can
produce 19 million
descendants in a
few days!!
Mosquitoes live 10-14
days laying eggs
every 3 days.
Mosquito rafts have
200-300 eggs;.
hatch in 48 hours
Reproductive potential – “K”
Some species have
higher reproductive
potential!!
K-Potential Gestation
Times:
Human= 9 months
Elephants= 22 months
Oppossum = 12-13
days (marsupial)
CRITICAL NUMBERS
Survival & recovery of population
depends on a minimum population
base—its critical number.
Factors Affecting Critical Number
C1. IMMIGRATION:
movement of indiv into an area
C2. EMIGRATION:
movement of individuals which leave
an area.
Plus
Environmental Resistance Factors
Critical Numbers
If pop falls below critical number,
breeding may fail and extinction could
occur.
Threatened: species whose pops are
declining rapidly
Endangered: near critical number and
may become extinct.
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