Population growth - exponential/geometric
Stochasticity and population growth
Population growth - logistic
Allee effects and population growth
Outline for this week
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
Habitat loss Pollution Overexploitation Exotic spp
Small fragmented isolated popn’s
Allee effects
Reduced N Demographic stochasticity
Env variation
Catastrophes Demographic processes
Stochastic processes
The ecology of small populations
Outline of this lecture
1 Recap logistic growth 2.! Describe allee effects
Graphically Empirical examples
3. Discuss conservation implications
Continuous dN = r0(1-N/K).N dt
Discrete
Exponential growth
Logistic growth Growth rate r = r0(1-N/K)
Nt+1 = Nt + Ntr0 1-Nt K
0
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
Coconut plantations ---> massive habitat destruction
1959 1 pop’n n=26 1968 Island bought by ICBP Managed as nature reserve
Coconut removed Forest regenerated
Seychelles warblers - endemic species to Seychelles Cousin Island
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)
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
Pop’n growth -ve +ve -ve
0
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
http://www.wildlifeextra.com/conch-imports129.html
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?
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
Pink ribbons Clarkia concinna
Isolation distance of patch (m)
Pollen
grai
ns
Seed s
et
(%)
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
Eg 3 cooperation among conspecifics increases fitness N
umber
of e
xtr
a hun
ts n
eeded
Pack size
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?
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
EG 4 cooperation among conspecifics increases fitness
Allee effects What causes them and how important are they?
cooperation among conspecifics increases fitness
Antipredator tactics are more efficient in large groups
Sentinel systems
Schooling behaviour Passive protection
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
Per capita growth rate dN/dt
K Pop’n size (N)
The allee effect
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
Unstable equilibrium stable equilibrium
Logistic growth Weak allee effect Strong allee effect
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?
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