Spartina alterniflora (Smooth cordgrass), native to the Altlantic coast, now invading Pacific coast estuaries:

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.

No

of

seed

s p

er f

low

er

No

of

ind

ivid

ual

s w

ith

see

d

Isolated Meadow

Different sites Different sites

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.

2) Increased predation risk at low density:• Losing the safety of numbers.

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;

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.

N0

dN Ndt

Warder. C. Allee(1885 – 1955)

Allee Effect:

N0

dN Ndt

1. Identify on this graph all population sizes where the population growth rate is zero.

2. Identify the range of population sizes over which population size increases.

3. Identify the range of population sizes over which population size decreases.

N0

dN dt

Stability analysis for model with Allee effect:

N0

dN dt

K0 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.

0*

0*

:

dt

dNthenNNif

dt

dNthenNNif

positivesmallFor

Stability analysis for model with Allee effect:

N0

dN dt

Unstable equilibrium

Stable equilibriumStable equilibrium

Density-dependence:

= the way that per-capita population growth rates depend on population sizes:

1) No density-dependence:

N0

dN Ndt

N0

dN Ndt

2) Negative density-dependence:(often created by competition)

Density-dependence:

= the way that per-capita population growth rates depend on population sizes:

N0

dN Ndt

3) Positive density-dependence:(often created by cooperation)

The sad story of the Passenger Pigeon:

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.

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.

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:

MARTHALast of her species, died at 1 p.m.,1 September 1914, age 29, in the

Cincinnati Zoological Garden.EXTINCT