Population growth - exponential/geometric Stochasticity and population growth Population growth - logistic Allee effects and population growth

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Population growth - exponential/geometric Stochasticity and population growth Population growth - logistic Allee effects and population growth

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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

explain what environmental and demographic stochasticity are

explain why stochasticity reduces expected population growth rates

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

Env variation

Allee effects

Demographic stochasticity

Reduced N

Demographic processes

Catastrophes

Stochastic processes

- Outline of this lecture
- 1 Recap logistic growth
- Describe allee effects
Graphically

Empirical examples

3. Discuss conservation implications

Exponential growth

0

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

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

Pop’n size (N)

K

The allee effect

Inverse density dependence at low densities

Warder Clyde Allee 1931,1949

Per capita growth rate

dN/dt

0

Pop’n size (N)

K

Pop’n growth -ve +ve -ve

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

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

Pink ribbons Clarkia concinna

Seed set (%)

Pollen grains

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

Eg 3 cooperation among conspecifics increases fitness

Number of extra hunts needed

Number of pups

Pack size

Allee effects

What causes them and how important are they?

EG 4 cooperation among conspecifics increases fitness

Lesser mole ratNaked 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

Males and females are more likely to emigrate if N is small

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?

Data31 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?