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?