Small population biology
Dr Peter Long
p.r.long@bath.ac.uk
Small populations
Mauritius kestrel
Hawaiian palm
Large blue
butterfly
Hainan gibbon
Sakalava rail
Black-footed
ferret
Why are small populations important?
-Population size is the single most important factor
affecting persistence or population viability
-Small populations are affected by small population
processes which can cause them to decline.
-Population size is an important criterion for
prioritisation
-Small populations are often found on islands
-Relevant to in-situ and ex-situ conservation
Approaches to species conservation
Declining population paradigm
Identify the causes of decline and
reverse threats.
Small population paradigm
Finding solutions to the problems
caused by small population size.
‘Conservation biology focuses on
managing small populations, and this
requires estimating their viability (or
vulnerability to extinction) so that
appropriate management action can be
taken.’
Lindenmayer (1993)
Extinction
Extinct
-Not reliably observed for 50 years
eg. Dodo
Extirpated
-Local extinction eg. Wolves in the UK
Extinct in the wild
-Not reliably observed for 50 years in the wild
-Ex-situ (zoos/botanic gardens) population
Eg. Wood’s cycad, Guam rail, Spix macaw, Smallpox
Extinction
Functionally extinct
-When only one individual (or one gender) remains
eg. Lonesome George
Ecologically extinct
-Present at such low density that has no impact on the
ecosystem eg. Javan rhinoceros
Rarity
Geographical range
Habitat specificity
Large
Small
Wide Narrow
Wide Narrow
Large population size
-
Rare
Rare
Rare
Small population size
Rare
Rare
Rare
Rarest
Rabinowitz (1981)
Lecture overview
- Important concepts in population biology
- Small population processes
- Introduction to conservation genetics
- Modelling small populations
- Diagnosing declines
Population dynamics
-
Births
Deaths
Emmigration
Immigration
Nt+1 = Nt + Births – Deaths + Emmigration - Immigration
These numbers are affected by both deterministic and
stochastic factors.
Deterministic factors
- Habitat loss
- Overexploitation
- Pollution
- Introduced species
- Chains of extinction
Stochastic factors
- Demographic
- Environmental
- Genetic
- Catastrophes
Population growth
•
•
•
•
If unlimited resources
dN/dt = Births-Deaths
dN/dt = rN
r = intrinsic rate of increase
• Intra-specific competition
for resources
• Per capita birth rate
decreases
• K = carrying capacity
• Growth rate depends on
population density
• ie ‘Density dependence’
r and K selection
A continuum that describes
life history patterns
r = intrinsic rate of increase
K = carrying capacity
r- and K-selecting habitats
r and K selected species
MacArthur & Wilson (1967)
r and K selected species
r selection
K selection
Rate of popn growth is
Rate of popn growth is
Limited by the environment Limited by reproductive rate
Small size eg. rat
Large size eg. elephant
Short lifespan
Long lifespan
Many offspring, little
investment in each
Few offspring, large
investment in each
Density dependence
Population density can affect competition for resources,
birth rates, death rates and dispersal.
Low density
More resources
per capita
High density
Fewer resources
per capita
Mortality relatively low
Mortality relatively high
Reproductive output
relatively high
(unless Allee effect)
Reproductive output
relatively low
Little disease
More disease
Rapid growth
Slow/negative growth
Survivorship
Limitation vs regulation
Do populations persist in the long term through stability
(populations are regulated) or through a series of setbacks and recovery (populations are limited)?
i.e. are density dependent or density-independent
factors the most important in controlling population
size?
Nicholson (1954) vs Andrewartha & Birch (1954)
A massive argument in ecology!
But these guys were arguing about separate processes
Limitation vs regulation
Limitation is the processes that set the population
equilibrium
Regulation is the process by which a population returns
to its equilibrium.
Regulation by definition occurs only as a result of one or
more density dependent processes that act on rates of
birth, death and/or movement through a negative
feedback mechanism
Population persistence requires that density dependent
processes operate - no population can be absolutely free
of regulation
In reality a combination of limiting and regulating factors
control populations
What does this mean in practice?
Food supply is primary factor determining
population growth rate.
But it can be over-ridden by three secondary
processes; predators, social interactions within
species and stochastic disturbances
Birds – food supply and social interactions
Large mammals – food supply and rarely
predation
Small mammals – predation and social
interactions
Fish, Herps and Inverts
– stochastic disturbances affecting
recruitment through food limitation
Metapopulations
• Landscapes tend to be
patchy
• A series of localised
populations linked by
dispersal
• Persistence occurs when
overall colonisation rates
exceed extinction rates
• Movement stabilises the
overall population
• Hanski (1991)
The extinction vortex
Deterministic factors
Habitat loss, Overexploitation, Pollution,
Introduced species, Chains of extinction
Small, fragmented,
isolated populations
Reduced reproduction
and survival
Inbreeding, loss of
genetic diversity
Increased disease
susceptibility
Small population processes
- Demographic stochasticity
- Environmental stochasticity
- Genetic stochasticity
- Catastrophes
-Allee effect
(negative density dependence)
-Special types of exploitation
(eg. Scarcity value and Bali starlings)
Demographic stochasticity
Variation in numbers of individuals of a particular age
and sex due to chance variation in birth and death
rates leads to variation in effective population size Ne.
Imagine a population of a monogamous species with
10 females and 3 males Nc = 13 Ne = 6.
It is also possible to estimate Ne over time and in
different breeding systems.
Demographic stochasticity
Eg.
- Sex-specific death rate eg 7 out of 9 Lord Howe
woodhen that died in a 2-year period in the 1980s
were female.
- Sex ratio eg Fiordland population of Kakapo in New
Zealand – 18 males persisted for 10 years after the
last female died. Extirpation in 1987. Merton (1989).
Environmental stochasticity
-Random environmental changes affect small
populations very severely.
- Climate eg. droughts, floods
- Variations in food abundance
- Effects of invasive species
eg. Mast-fruiting in Dipterocarps affects frugivores in
SE Asian forests.
Eg. Periodic bamboo flowering and giant pandas.
Genetic stochasticity
Small populations have low genetic diversity (allelic
diversity and heterozygosity).
Founder effects
There is only a limited sub-set of genes in founder
individuals.
Genetic bottlenecks
Populations that go through a contraction lose the
unique genes present on those that die without
reproducing.
Genetic drift
Random loss of genes between generations.
Increased chance of inbreeding
Raises homozygosity, deleterious genes
more likely to be expressed.
Genetic stochasticity
Fisher’s fundamental theorem
Rate of evolutionary change is proportional to genetic
diversity in a population.
Deleterious genes…
-Are usually recessive
-Reduce inclusive fitness
-Are more likely to be expressed when
mating occurs between relatives.
Eg. A skeletal disorder, Chondrodystrophy in
California condors caused by a recessive
autosomal allele.
Catastrophes
- Volcanic eruptions eg Montserrat
- Cyclones eg Indian ocean islands
- Lightning strikes/severe fires
N.B can occur at a range of spatial scales
Allee effects
-Negative population growth at low
population densities due to
disruption of interaction between
individuals.
- eg. Puerto Rican parrots only
reproduce in colonies. When
population density fell below a
particular threshold there was no
reproduction.
-eg. Brown bears and cougars occur
at very low densities in N. America.
Often hard to physically find a mate.
-Possibly also a problem for blue
whales
Conservation genetics
The science of the genetic factors that affect extinction risk and
the management actions which can minimise these risks.
Concept map
Evolutionary
genetics
Understanding
species biology
Forensics
Genetic
management
Taxonomic
uncertainty
Population structure
(fragmentation)
Conservation genetics
Outbreeding
Small populations
Inbreeding
Loss of genetic diversity
Fitness
Extinction
Identification of management
units in wild and/or captivity
Introgression
Reintroductions
Mutational accumulation
Uses of conservation genetics
- Reducing extinction risk by minimizing loss of
genetic diversity
Eg. Captive management of Golden Lion Tamarin,
Management of wild Florida panthers
- Identifying populations of concern
Eg. Asiatic lions, Wollemi pine
- Resolving population structure
Eg. Red-cockaded woodpecker
- Resolving taxonomic uncertainty
Eg. Tuataras, Velvet worms
- Defining management units
Eg. Kentish plover/Snowy plover
Uses of conservation genetics
- Detecting hybridisation
Eg. Many plants, salmonid fish, Ethiopian wolf
- Non-intrusive sampling
Eg. Giant pandas
- Defining sites for re-introductions
Eg. Northern hairy-nosed wombat, Laysan duck
-
Choosing populations for re-introductions
Eg. Black-footed wallabies
-
Forensics
Eg. Whales
- Understanding species biology
Eg. Chimpanzees
Modelling small populations
Three approaches:
- Population models (consider total population size)
Eg r models
- Matrix models (consider numbers in age classes)
Eg Leslie matrices
- Individual models (consider every individual)
-Eg VORTEX
An example of a population model
The imaginary parrot is endemic to a small island.
We can use data on total population size in a time series
to estimate r, the intrinsic rate of increase.
N.B. Made-up data and simplifying assumptions.
Year (t) Population (N)
2000
2632
2001
2132
2002
1954
2003
1900
2004
1638
2005
1612
Decline of the imaginary parrot
Population size (N)
3000
2500
2000
1500
1000
500
0
2000
2001
2002
2003
Year (t)
2004
2005
What is r?
r is the intrinsic rate of population growth.
If r is 0 the population is stationary,
if r is positive the population is growing,
if r is negative the population is declining.
For declining populations, we are interested in the mean r
value and its variance. The magnitude of r measures the rate
of decline. The variance in r measures how stochastic this
decline is.
The antilog of r is net survival (the proportion of individuals
that survive each year).
The r value lets you estimate the population size in the future.
How to calculate r
dN
= rN
dt
Exponential model of population growth
N t = N t −1e r
N t / N t −1 = e r
Expressed as number (N) at time t
r = ln( N t / N t −1 )
Make r the subject
Re-arranged
Year(t)
2000
2001
N
2632
2132
lnN
7.875
7.665
Nt/Nt-1
r=ln(Nt/Nt-1)
0.810
-0.211
2002
2003
2004
2005
1954
1900
1638
1612
7.578
7.550
7.401
7.385
0.917
0.972
0.862
0.984
-0.087
-0.028
-0.148
-0.016
r = -0.098
What can we do with this?
r = -0.098
You can take the antilog to get net survival.
Net survival = e-0.098 = 0.907
This means that only 91% of the parrots alive in year t will be
alive in year t+1
To work out the population size n years in the future use:
Nt+n = Nt * net survival n
Eg. How many will there be in 2008?
Our latest estimate for the population size, Nt is 16122005
N2005+3 = 16122005 * 0.9073 = 1203
So when will the parrot go extinct?
The parrot is functionally extinct when Nt+n= 1 Net survival=0.907
Our latest estimate for the population size Nt = 16122005
Substituting and solving for n, we can find when the parrot goes extinct:
N t +n = N t * Net survival n
1 = 1612 20050.907 n
1
= 0.907 n
1612 2005
⎛
⎞
1
⎟⎟ = n ln 0.907
ln⎜⎜
⎝ 1612 2005 ⎠
⎛
⎞
1
⎟⎟
ln⎜⎜
1612 2005 ⎠
⎝
n=
= 76
ln 0.907
2005 + 76 = 2081
Matrix models
eg. Leslie matrices
Consider numbers of individuals in a several age classes.
Estimate net survivorship in each age class over each time
period. Eg. What proportion of parrots survive their first year?
What proportion survive their second year? Etc.
Models of total population size
assume Type II survivorship
(linear). Matrix models can
incorporate other, more realistic,
types of suvivourship eg. Type I
(r-selected species) or Type III
(K-selected species).
Deterministic vs stochastic models
A deterministic model gives a definite answer.
A stochastic model gives an answer and a confidence
interval which reflects uncertainty in the data.
Deterministic model
Stochastic model
Nt=100
Nt=100
+12 births
-6 deaths
+12±3 births
-6±2 deaths
Nt+1=106
Nt+1=106±5
(display as a histogram)
Individual models
Eg VORTEX, RAMAS, GAPPS
Individual-based models
Inputs:
-Life-history
-Age structure
-Inbreeding depression
-Environmental variation
-Catastrophes
-Carrying capacity
-Threats
Stochastic population model
Outputs:
-Population size
-Probability of viability
-Loss of genetic diversity
For a review see
Coulson et al. (2001)
Can use VORTEX to model persistence
under different management scenarios
(Sommer et al. 2002)
Diagnosing declines
• Manipulate factor to
achieve population
growth
• Very difficult!
• Mechanistic and
density paradigms
• Experimental
conservation biology
and evidence-based
conservation
Monitoring
programme
Analysis
Population growth rate
• Vital for conservation
Factor of decline
Species management
actions
Diagnosing causes of decline
Lord Howe woodhen is a flightless rail
endemic to Lord Howe island (25km2).
Settled in 1834 and dogs, pigs, rats
were introduced. Woodhens became
confined to two mountainous summits
surrounded by sheer cliffs. Sub-optimal
habitat.
In 1969 monitoring started. 20-25
individuals. Low productivity. Very wet
winter in 1978. In 1980 only 12
individuals on Mt. Gower.
Why was productivity low? Rats, cats,
owls, pigs? Detailed studies showed
pigs were limiting. 180 pigs shot.
Intensive management led to recovery.
Miller & Mullette (1985)
Summary: risk factors
- Island endemics/restricted range
eg. Mauritius kestrel
- K strategists
eg. Rhinos
- Species at high trophic levels
eg. Big cats
- Allee effect susceptible species
eg. Puerto Rican parrot
- Species with large home ranges
eg. jaguars
- Species susceptible to hunting
eg. duikers
- Niche specialists
eg. Spotted owls
Further reading
Pullin (2002)
Chapter 10
Groom et al. (2005) Caughley &
Chapters 11 and 12 Gunn (1996)
Chapters 6,
7, 8 and 9
Frankham, Ballou
& Briscoe (2002)
Chapters 1, 10
References
Rarity
Rabinowitz, D. (1981) Seven forms of rarity. The biological aspects of plant conservation. Wiley.
Conservation biology paradigms
* Caughley G (1994) Directions in conservation biology. Journal of Animal Ecology 63: 215-244
Population dynamics
Sibly, R.M., J. Hone & T.H. Clutton-Brock. (2003) Wildlife Population Growth Rates. Cambridge University Press,
UK.
* Sinclair, A.R.E. (1989) Population regulation in animals. In. Ecological Concepts (ed JM Cherrett). pp197-242.
Blackwell Scientific Publications, Oxford
Sinclair, A.R.E. & Pech, R.P., Dickman, C.R., Hik, D., Mahon, P. & Newsome, A.E. (1998) Predicting the effects of
predation on conservation of endangered prey. Conservation Biology, 12, 564-575.
Metapopulations
Hanski, I. (1999) Metapopulation Ecology. Oxford University Press, Oxford
Small populations
Miller B, Mulltee KJ (1985) Rehabilitation of an endangered Australian bird: the Lord Howe island woodhen
Tricholimnas sylvestris (Sclater). Biological Conservation 34: 55-95
Genetics
Frankham R, Ballou JD, Briscoe DA (2002) Introduction to conservation genetics. Cambridge University Press.
Population models
Coulson T, Mace GM, Hudson E, Possingham H, (2001) The use and abuse of population viability analysis.
Trends in Ecology and Evolution 16(5): 219-221