population growth - exponential/geometric stochasticity and population growth population growth -...
TRANSCRIPT
Population growth - exponential/geometric
Stochasticity and population growth
Population growth - logistic
Allee effects and population growth
Outline for this week
Last lectureyou should be able to a)explain what environmental and
demographic stochasticity areb)explain why stochasticity reduces
expected population growth ratesc) discuss the implications of
stochastic processes for small populations
Habitat loss Pollution Overexploitation Exotic spp
Small fragmented isolated popn’s
Allee effects
Reduced NDemographic stochasticity
Env variation
CatastrophesDemographic processes
Stochastic processes
The ecology of small populations
Outline of this lecture
1 Recap logistic growth2. Describe allee effects
GraphicallyEmpirical 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=261968 Island bought by ICBPManaged 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 ratedN/dt
K Pop’n size (N)
Per capita growth ratedN/dt
K Pop’n size (N)
The allee effectInverse density dependence at low densities
Warder Clyde Allee 1931,1949
Pop’n growth -ve +ve -ve
0
Allee effectsWhat causes them and how important are they?
1. Inbreeding and loss of heterozygosity2. Demographic stochasticity3. 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 ConchShells >30 cm Heavily harvestedFisheries closed Bermuda 1978
Florida 1986Illegal fishing continuesFishing allowed in Caribbean
Stocks have not recovered
Appeldoorn 1988 - could this be due to an allee effect?
Stoner and Ray-Culp 2000Bahamas - 2 areas 54 sites density 2-812 conch ha-1
- assessed reproductive activity
Conc’n?
Allee effectsWhat causes them and how important are they?
Eg 2- a reduced ability to reproduce - indirect
Pink ribbons Clarkia concinna
Isolation distance of patch (m)
Polle
n g
rain
s
Seed
set
(%)
In large patches pollen grain number or seed set does not decline with isolation. Q. What could be happening?
Allee effectsWhat causes them and how important are they?
Eg 3 cooperation among conspecifics increases fitness
African wild dogs
IUCN Endangeredca 3000 left
Packs 6-20 adults1 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 fitnessN
um
ber
of
extr
a h
un
ts n
eed
ed
Pack size
Num
ber o
f pup
s
Allee effectsWhat causes them and how important are they?
EG 4 cooperation among conspecifics increases fitness
Lesser mole rat Naked mole rat
Allee effectsWhat causes them and how important are they?
Mole-rats are extremely socialFood is cached and shared among colony membersThe ability to find food increases with colony sizeSmall colonies are more likely to fail
Jarvis et al. 1998
EG 4 cooperation among conspecifics increases fitness
Allee effectsWhat 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 effectsWhat 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 increasesFertilization rates/seed set increasesForaging success increases with group sizeAntipredator strategies are more effectiveAbility to modify environment improves
Per capita growth ratedN/dt
KPop’n size (N)
The allee effect
Conservation implicationsWhere the allee effect is strong models predict a lower unstable equilibrium population sizeBelow the lower equilibrium populations will decline
to extinction
Unstable equilibrium stable equilibrium
Logistic growthWeak allee effectStrong 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?