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?