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Spartina alterniflora (Smooth cordgrass), native to the
Altlantic coast, now invading Pacific coast estuaries:
No of seeds per flower
No of individuals with seed
Isolated
Meadow
Different sites
Different sites
Seed set of plants at the low density leading edge of the invasion
was reduced to 1/8th compared to pants within meadows of Spartina.
From Davis et al. 2004
The Mauna Kea silversword is extremely rare and
cannot self.
Silversword
Alliance:
30 species in 3
genera, the
descendents of
possibly a single
introduction.
Haleakaka
silversword:near
extinction
•
•
•
good to eat
do not self
recruit rarely
By 1970’s, only 42 individual
plants were left, clinging on to
cliffs and rock faces
inaccessible to sheep.
Animals grouping
together to lower the
risk of predation
Big horn sheep have a very high predation
risk from mountain lion, bobcat, coyote.
They spend a large amount of time and
energy on looking out for predators.
From Mooring et al. 2004
The African hunting dog, Africa’s most endangered
large carnivore:
Adults live in same-sex packs of up to six individuals.
When they meet a group of opposite sex, they form a new group.
However, only one pair will breed, the others hunt and look after the young.
The biology behind the Allee effect:
1) Reproductive challenges at low density:
• Males and females rarely meet (compatible male and
female gametes rarely meet);
• Inbreeding depression;
2) Increased predation risk at low density:
• Losing the safety of numbers.
3) Cooperative behavior suffers at low density:
• 10 eyes see more than 2;
• No one to hunt with;
• No one to look after the kids (cooperative breeding).
Allee Effect:
When populations at low numbers have a
positive relationship between per-capita
population growth rate and population density.
Warder. C. Allee
(1885 – 1955)
dN
Ndt
0
N
Allee Effect:
dN
Ndt
0
N
1. Identify on this graph all
population sizes where the
population growth rate is zero.
dN
dt
2. Identify the range of population
sizes over which population
size increases.
0
N
3. Identify the range of population
sizes over which population
size decreases.
Stability analysis for model with Allee effect:
dN
dt
0
K0
N
K
Plug & Play
Excel Worksheets:
• Allee Effect
Definition of an “unstable equilibrium” in population
dynamics:
An equilibrium N* is said to be locally unstable if
population sizes that are slightly smaller or slightly
bigger move away from the equilibrium state.
For small positive  :
if
N  N * 
then
if
N  N * 
then
dN
0
dt
dN
0
dt
Stability analysis for model with Allee effect:
dN
dt
0
N
Unstable equilibrium
Stable equilibrium
Stable equilibrium
Density-dependence:
= the way that per-capita population growth rates
depend on population sizes:
dN
Ndt
1) No density-dependence:
0
2) Negative density-dependence:
(often created by competition)
N
dN
Ndt
0
N
Density-dependence:
= the way that per-capita population growth rates
depend on population sizes:
3) Positive density-dependence:
(often created by cooperation)
dN
Ndt
0
N
The sad story of the Passenger Pigeon:
In the early 18th century, at an estimated 3 – 5 billion, the
passenger pigeon may have been the most abundant bird
species that ever lived.
By the late 1889 there were no more
free-living flocks.
The last known individual, a female
called Martha, died in 1914 in the
Cincinnati Zoo.
The sad story of the Passenger Pigeon:
The last known individual of the passenger pigeon species was
"Martha" (named after Martha Washington). She died at the
Cincinnati Zoological Garden, and was donated to the Smithsonian
Institution, where her body was once mounted in a display case with
this notation:
MARTHA
Last of her species, died at 1 p.m.,
1 September 1914, age 29, in the
Cincinnati Zoological Garden.
EXTINCT