Outline for this week
Population growth exponential/geometric
Stochasticity and population growth
Population growth logistic
Allee effects and population growth
Last lecture
you should be able to
a)! explain what environmental and
demographic stochasticity are
b)!explain why stochasticity reduces
expected population growth rates
c)! discuss the implications of stochastic
processes for small populations
The ecology of small populations
Habitat loss Pollution Overexploitation Exotic spp
Small
fragmented
isolated popn’s
Allee effects
Reduced N
Demographic processes
Env variation
Demographic
stochasticity
Catastrophes
Stochastic processes
Outline of this lecture
1 Recap logistic growth
2.! Describe allee effects
Graphically
Empirical examples
3. Discuss conservation implications
Exponential growth
0
Logistic growth
Growth rate r = r0(1-N/K)
Continuous
Discrete
dN = r0(1-N/K).N
dt
Nt+1 = Nt + Ntr0 1-Nt
K
Biological interpretation
r0 can be interpreted as population growth in the
absence of intra-specific competition
r0 is the maximum per capita rate of growth
K is the upper limit of population growth
K is the carrying capacity ie the maximum pop’n size that
can be supported by the available resources
1-N/K - unused portion of the carrying capacity
Seychelles warblers - endemic species to Seychelles
Cousin Island
Coconut plantations --->
massive habitat destruction
1959 1 pop’n n=26
1968 Island bought by ICBP
Managed as nature reserve
Coconut removed
Forest regenerated
Logistic population growth
What happens to the per capita growth rate as N increases?
Per capita growth rate
dN/dt
K
Pop’n size (N)
The allee effect
Inverse density dependence at low densities
Warder Clyde Allee 1931,1949
Per capita growth rate
dN/dt
0
Pop’n growth -ve
Pop’n size (N)
K
+ve
-ve
Allee effects
What causes them and how important are they?
1.! Inbreeding and loss of heterozygosity
2.! Demographic stochasticity
3.! A shortage of interactions among conspecifics at low
densities
Allee effects
EG 1 - reduced opportunities to reproduce
Caribbean Queen Conch
Shells >30 cm
Heavily harvested
Fisheries closed Bermuda 1978
Florida 1986
Illegal fishing continues
Fishing allowed in Caribbean
Stocks have not recovered
Appeldoorn 1988 - could this be
due to an allee effect?
http://www.wildlifeextra.com/conch-imports129.html
Stoner and Ray-Culp 2000
Bahamas
- 2 areas 54 sites density 2-812 conch ha-1
- assessed reproductive activity
Conc’n?
Allee effects
What causes them and how important are they?
Eg 2- a reduced ability to reproduce - indirect
Seed set (%)
Pollen grains
Pink ribbons Clarkia concinna
Isolation distance of patch (m)
In large patches pollen grain number or seed set does not decline
with isolation.
Q. What could be happening?
Allee effects
What causes them and how important are they?
Eg 3 cooperation among conspecifics increases fitness
African wild dogs
IUCN Endangered
ca 3000 left
Packs 6-20 adults
1 breeding pair
Litters 2-20 pups
Eg 3 cooperation among conspecifics increases fitness
Foraging success increases with pack size
Number of extra hunts needed
Eg 3 cooperation among conspecifics increases fitness
Pack si
ze
Allee effects
What causes them and how important are they?
EG 4 cooperation among conspecifics increases fitness
Lesser mole rat
Naked mole rat
Allee effects
What causes them and how important are they?
EG 4 cooperation among conspecifics increases fitness
Mole-rats are extremely
social
Food is cached and shared
among colony members
The ability to find food
increases with colony size
Small colonies are more
likely to fail
Jarvis et al. 1998
Allee effects
What causes them and how important are they?
cooperation among conspecifics increases fitness
Sentinel systems
Schooling behaviour
Passive protection
Antipredator tactics are more efficient in
large groups
Allee effects
What causes them and how important are they?
EG 5 modification of the environment is density dependent
At low densities, hemlock is less
able to acidify soil and sequester
water in the upper soil horizons.
Production thus increases with
density
Allee effects
Mechanisms leading to +ve relationship
between
population size and individual fitness
Ability to locate a mate increases
Fertilization rates/seed set increases
Foraging success increases with group size
Antipredator strategies are more
effective
Ability to modify environment improves
The allee effect
Logistic growth
Weak allee effect
Strong allee effect
Per capita growth rate
dN/dt
K
Pop’n size (N)
Unstable equilibrium
stable equilibrium
Conservation implications
Where the allee effect is strong models predict a lower
unstable equilibrium population size
Below the lower equilibrium populations will decline to
extinction
Are allee effects strong enough to impact
population dynamics?
Glanville fritillary
- found in dry meadow
- 300-500 of possible 1500
suitable patches occupied
Evidence for Allee effect
1.! Males and females are more
likely to emigrate if N is
small
2.! See Fig
Kuussaarri et al 1998 Oikos
Are allee effects strong enough to impact
population dynamics?
What influences whether a pop’n grows?
Discuss
Are allee effects strong enough to impact
population dynamics?
Taylor et al 2005 Animal Conservation 8: 415-20
Does founder size of Saddleback and New Zealand robin influence the
success of reintroductions?
Data
31 reintroductions to offshore islands
Numbers released ranged from 5- 188
Are allee effects strong enough to impact
population dynamics?
Taylor et al 2005 Animal Conservation 8: 415-20
Does founder size of Saddleback and New Zealand robin influence the
success of reintroductions?
NO
SUMMARY
Evidence for allee effects exists for diverse
taxa
Allee effects reduce population growth at
low densities
Allee effects can influence population
dynamics and may increase extinction risk
Q What spp are most likely to be affected?