Population%20growth%20-%20exponential/geometric

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Outline for this week
Population growth - exponential/geometric Sto
chasticity and population growth Population
growth - logistic Allee effects and
population growth
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• 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

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The ecology of small populations

Habitat loss Pollution Overexploitation Exotic spp
Small fragmented isolated popns
Env variation
Allee effects
Demographic stochasticity
Reduced N
Demographic processes
Catastrophes
Stochastic processes
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• Outline of this lecture
• 1 Recap logistic growth
• Describe allee effects
• Graphically
• Empirical examples
• 3. Discuss conservation implications

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Exponential growth
0
Logistic growth
Growth rate r r0(1-N/K)
Continuous dN r0(1-N/K).N
dt Discrete
Nt1 Nt Ntr0 1-Nt K
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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 popn size that can be supported by
the available resources 1-N/K - unused portion
of the carrying capacity
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Seychelles warblers - endemic species to
Seychelles Cousin Island
Coconut plantations ---gt massive habitat
destruction 1959 1 popn n26 1968 Island bought
by ICBP Managed as nature reserve Coconut
removed Forest regenerated
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Logistic population growth
What happens to the per capita growth rate as N
increases?
Per capita growth rate dN/dt
Popn size (N)
K
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The allee effect Inverse density dependence at
low densities
Warder Clyde Allee 1931,1949
Per capita growth rate dN/dt
0
Popn size (N)
K
Popn growth -ve ve -ve
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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

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Allee effects
EG 1 - reduced opportunities to reproduce
Caribbean Queen Conch Shells gt30 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
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Stoner and Ray-Culp 2000 Bahamas - 2 areas 54
sites density 2-812 conch ha-1 - assessed
reproductive activity
Concn?
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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 ()
Isolation distance of patch (m)
In large patches pollen grain number or seed set
does not decline with isolation. Q. What
could be happening?
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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
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Eg 3 cooperation among conspecifics increases
fitness
Foraging success increases with pack size
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Eg 3 cooperation among conspecifics increases
fitness
Number of extra hunts needed
Number of pups
Pack size
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Allee effects What causes them and how important
are they?
EG 4 cooperation among conspecifics increases
fitness
Lesser mole rat Naked mole rat
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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
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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
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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
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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
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The allee effect
Logistic growth Weak allee effect Strong allee
effect
Per capita growth rate dN/dt
K
Popn 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
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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
• Males and females are more likely to emigrate if
  N is small
• See Fig

Kuussaarri et al 1998 Oikos
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Are allee effects strong enough to impact
population dynamics?
What influences whether a popn grows?
Discuss
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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
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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
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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?