Download Population Growth Curves

Ecology: Population Ecology
POPULATIONS
3.
A population
is a group of
individuals of
the same
species
living in an
area
2
DISTRIBUTION PATTERNS
Populations disperse in a variety of ways that
are influenced by environmental and social
factors
• Uniform distribution results from
intense competition or antagonism
between individuals.
• Random distribution occurs when
there is no competition,
antagonism, or tendency to
aggregate.
• Clumping is the most common
distribution because environmental
conditions are seldom uniform.
3
What causes these populations of different organisms
to clump together?
Clumped distribution
in species acts as a
mechanism against
predation as well as an
efficient mechanism to
trap or corner prey. It
has been shown that
larger packs of animals
tend to have a greater
number of successful
kills.
Fig. 52.1, Campbell & Reece, 6th ed.
POPULATION DISPERSAL
• In rare cases, long-distance dispersal can lead to adaptive radiation
• For example, Hawaiian silverswords are a diverse group descended
from an ancestral North American tarweed
5
THE SPREAD OF THE
AFRICANIZED HONEY
BEE
WHEN DID THEY FIRST
ARRIVE IN THE
AMERICAS?
HOW LONG DID IT TAKE
FOR THEM TO EXPAND
THEIR RANGE INTO THE
US?
HOW CAN YOU EXPLAIN
THEIR SUCCESS IN
EXPANDING THEIR
6
TERRITORY?
SMALL GEOGRAPHIC RANGE
7
SPECIES WITH A LARGE GEOGRAPHIC RANGE
8
ESTIMATING POPULATION SIZE
THE MARK-AND-RECAPTURE TECHNIQUE
2.
1.
3.
9
ESTIMATING POPULATION SIZE
THE MARK-AND-RECAPTURE TECHNIQUE
• There’s a simple formula for estimating the total population size
𝑠 𝑥
=
𝑁 𝑛
s = Number
of individuals marked and released in 1st sample
x = Number
of individuals marked and released in 2nd sample
n = Total
number of individuals in 2nd sample
N = Estimated
population size
Rearrange to get:
𝑁=
𝑠𝑛
𝑥
10
LET’S TRY AN EXAMPLE!
• Twenty individuals are captured at random and marked with a
dye or tag and then are released back into the environment.
• Therefore s = # of animals marked = 20
• At a later time a second group of animals is captured at
random from the population. Some will already be marked,
say 10 individuals were marked out of 35 that were captured
the second time. We now know n = 35 and x = 10
𝑠𝑛
• Remember:
𝑁=
𝑥
11
• So, apply the formula and solve for the estimated population size:
𝑁=
𝑠𝑛
𝑥
=
20 35
10
=
700
=
10
70
Therefore, N = 70 as a population estimate
12
WHICH METHOD WOULD YOU USE?
1. To determine the number of deer in the state of
Virginia?
2. To determine the number of turkeys in a county?
3. To determine the number of dogs in your
neighborhood?
4. To determine the number of ferrel cats in your
neighborhood?
13
SURVIVORSHIP CURVES
1000
What do these graphs
indicate regarding species
survival rate & strategy?
Human
(type I)
I. High death rate in
post-reproductive
years
Hydra
(type II)
Survival per thousand
100
II. Constant mortality rate
throughout life span
Oyster
(type III)
10
1
0
25
50
75
Percent of maximum life span
100
III. Very high early
mortality but the few
survivors then live long
(stay reproductive)
POPULATION GROWTH CURVES
𝑑𝑁
=𝐵−𝐷
𝑑𝑡
d = delta or change
N = population Size
t = time
B = birth rate
D =death rate
r=
𝐵 −𝐷
𝑁
15
POPULATION GROWTH MODELS
Exponential model (blue)
idealized population in an unlimited
environment (J-curve); can’t continue
indefinitely.
r-selected species (r = per capita
growth rate)
𝒅𝑵
= 𝒓𝒎𝒂𝒙 𝑵
𝒅𝒕
Logistic model (red) considers
population density on growth
(S-curve), carrying capacity (K):
maximum population size that a
particular environment can support;
K-selected species
𝒅𝑵
𝑲−𝑵
= 𝒓𝒎𝒂𝒙 𝑵
𝒅𝒕
𝑲
EXPONENTIAL GROWTH CURVES
Growth Rate of E. coli
d = delta or change
N = Population Size
t = time
rmax = maximum per
capita growth rate
of population
Population Size, N
𝒅𝑵
= 𝒓𝒎𝒂𝒙 𝑵
𝒅𝒕
Time (hours)
17
LOGISTIC GROWTH CURVES
• In the logistic population growth model, the per
capita rate of increase (rmax) declines as carrying
capacity (K) is reached
• The logistic model starts with the exponential
model and adds an expression that reduces per
capita rate of increase as N approaches K
𝑑𝑁
𝐾−𝑁
= 𝑟𝑚𝑎𝑥 𝑁
𝑑𝑡
𝐾
18
LOGISTIC GROWTH CURVES
𝒅𝑵
𝑲−𝑵
= 𝒓𝒎𝒂𝒙 𝑵
𝒅𝒕
𝑲
d = delta or change
N = Population Size
t = time
K =carrying capacity
rmax = maximum per
capita growth rate
of population
19
COMPARISON OF GROWTH CURVES
20
GROWTH CURVE RELATIONSHIP
21
EXAMINING LOGISTIC POPULATION
GROWTH
22
EXAMINING LOGISTIC POPULATION GROWTH
Hypothetical Example of Logistic Growth Curve
K = 1,000 & rmax = 0.05 per Individual per Year
23
POPULATION REPRODUCTIVE STRATEGIES
• r-selected
(opportunistic)
• Short maturation & lifespan
• Many (small) offspring;
1 (early) reproduction;
• No parental care
• High death rate
• K-selected
(equilibrial)
usually • Long maturation & lifespan
• Few (large) offspring;
usually several (late)
reproductions
• Extensive parental care
• Low death rate
How Well Do These Organisms Fit the
Logistic Growth Model?
Some populations overshoot K
before settling down to a
relatively stable density
Some populations fluctuate greatly and
make it difficult to define K
25
Age Structure Diagrams: Always Examine The Base Before
Making Predictions About The Future Of The Population
Rapid growth
Afghanistan
Male
Female
10 8
6 4 2 0 2 4 6
Percent of population
Age
85+
80–84
75–79
70–74
65–69
60–64
55–59
50–54
45–49
40–44
35–39
30–34
25–29
20–24
15–19
10–14
5–9
0–4
8 10
8
Slow growth
United States
Male
Female
6 4 2 0 2 4 6
Percent of population
Age
85+
80–84
75–79
70–74
65–69
60–64
55–59
50–54
45–49
40–44
35–39
30–34
25–29
20–24
15–19
10–14
5–9
0–4
8
8
No growth
Italy
Male
Female
6 4 2 0 2 4 6 8
Percent of population