1. Outline for this week
Population growth exponential/geometric
Stochasticity and population growth
Population growth logistic
Allee effects and population growth

2. Last lecture
you should be able to
explain what environmental and demographic stochasticity are
explain why stochasticity reduces expected population growth rates
discuss the implications of stochastic processes for small populations

3. The ecology of small populations
Habitat loss Pollution Overexploitation Exotic spp
Small fragmented isolated popn’s
Env variation
Allee effects
Demographic stochasticity
Reduced N
Demographic processes
Catastrophes
Stochastic processes

4. Outline of this lecture
1 Recap logistic growth
Describe allee effects
Graphically
Empirical examples
3. Discuss conservation implications

5. Exponential growth Logistic growth Growth rate r = r0(1-N/K)
Logistic growth
Growth rate r = r0(1-N/K)
Continuous dN = r0(1-N/K).N dt
Discrete
Nt+1 = Nt + Ntr0 1-Nt K

6. 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

7. Seychelles warblers - endemic species to Seychelles Cousin Island
Coconut plantations --->
massive habitat destruction
pop’n n=26
1968 Island bought by ICBP
Managed as nature reserve
Coconut removed
Forest regenerated
birds to Aride Island
birds to Cousine Island

8. Logistic population growth
What happens to the per capita growth rate as N increases?
Per capita growth rate
dN/dt
Pop’n size (N) K

9. Inverse density dependence at low densities
The allee effect
Inverse density dependence at low densities
Warder Clyde Allee 1931,1949
Per capita growth rate
dN/dt
Pop’n size (N) K
Pop’n growth -ve ve -ve

10. What causes them and how important are they?
Allee effects
What causes them and how important are they?
Inbreeding and loss of heterozygosity
Demographic stochasticity
A shortage of interactions among conspecifics at low densities

11. 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 could this be due to an allee effect?
Stoner and Ray-Culp (2000) Evidence for Allee effects in an over-harvested marine gastropod: density dependent mating and egg production Mar Ecol Prog Series 202:

12. Conc’n? Stoner and Ray-Culp 2000
Bahamas - 2 areas 54 sites density conch ha-1
- assessed reproductive activity
Stoner and Ray-Culp (2000) Evidence for Allee effects in an over-harvested marine gastropod: density dependent mating and egg production Mar Ecol Prog Series 202:
Conc’n?

13. What causes them and how important are they?
Allee effects
What causes them and how important are they?
Eg 2- a reduced ability to reproduce - indirect
Pink ribbons Clarkia concinna
Pollen grains
Seed set (%)
Groom 1998
Isolation distance of patch (m)
In large patches pollen grain number or seed set does not decline with isolation. Q. What could be happening?

14. What causes them and how important are they?
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

15. Eg 3 cooperation among conspecifics increases fitness
Foraging success increases with pack size

16. Eg 3 cooperation among conspecifics increases fitness
Number of extra hunts needed
Courchamp et al (2002) Small pack size imposes a trade-off between hunting and pup guarding in the painted hunting dog Behav Ecol 13: 20-27
Number of pups
Pack size

17. What causes them and how important are they?
Allee effects
What causes them and how important are they?
EG 4 cooperation among conspecifics increases fitness
Lesser mole rat Naked mole rat

18. What causes them and how important are they?
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

19. What causes them and how important are they?
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

20. What causes them and how important are they?
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

21. 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

22. The allee effect K Unstable equilibrium stable equilibrium
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

23. Are allee effects strong enough to impact population dynamics?
Glanville fritillary
- found in dry meadow
of possible 1500 suitable patches occupied
Evidence for Allee effect
Males and females are more likely to emigrate if N is small
See Fig
Kuussaarri et al 1998 Oikos

24. Discuss Are allee effects strong enough to impact population dynamics?
What influences whether a pop’n grows?
Discuss

25. Are allee effects strong enough to impact population dynamics?
Taylor et al 2005 Animal Conservation 8:
Does founder size of Saddleback and New Zealand robin influence the success of reintroductions?
Taylor, SS et al. (2005). Successful island reintroductions of New Zealand robins and saddlebacks with small numbers of founders
ANIMAL CONSERVATION 8:
Data 31 reintroductions to offshore islands
Numbers released ranged from

26. NO Are allee effects strong enough to impact population dynamics?
Taylor et al 2005 Animal Conservation 8:
Does founder size of Saddleback and New Zealand robin influence the success of reintroductions?
Taylor, SS et al. (2005). Successful island reintroductions of New Zealand robins and saddlebacks with small numbers of founders
ANIMAL CONSERVATION 8: NO

27. Evidence for allee effects exists for diverse taxa
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?