Transcript Life History and Demography - UC Davis: Environmental

Population Viability Analysis
Conservation Planning
• U.S. Endangered Species Act mandates
two processes
– Habitat Conservation Plans
– Recovery Plans
• Quantitative methods are needed to
assess viability of threatened and
endangered populations in these plans
• Population viability analysis is a set of
tools for quantifying the current and future
status of population of conservation
interest
Population Viability Analysis
• Differ significantly from traditional fisheries
populations models
• Prediction of population growth or decline
• Quantitative methods to predict probability or
time to extinction
• Predict which life stages contribute most to
population growth
• Assess affects of variation in vital rates on
prediction capabilities
• Determining which additional data are most
needed to improve future population estimate
Population Viability Analysis
• Prediction of time to extinction given
current status
• Predict how different management
strategies will affect extinction probability
• Predict how many individuals would be
needed to establish a new population
• Predict what harvest limits would still
permit population growth (or stability)
• Predict how many populations are needed
to prevent global extinction
Analyzing Monitoring Data
• PVAs can be used to integrate and analyze
monitoring data
– Recovery plans specify that survival, growth and
reproduction of populations be monitored
– Habitat conservation plans also require monitoring of
populations at some level, although requirements
vary
• Often the use of these data is not specified and
data are not always used to aid recovery or
evaluate HCPs
Vital Rates
• Like most demographic analyses, PVAs focus on key
birth and death processes
• Simpler models ignore immigration and emigration
(although more complicated ones can include multiple
populations with migration)
• Survival
– Typically refers to remaining in an stage class (age class)
• Growth
– Typically refers to going from one stage class (age class) to
another
• Reproduction
– Typically refers to number of offspring per individual (usually
female)
Estimating Population Growth
• Vital rates determine rate of population growth
• Population size at time “t” is Nt
• Population size at some later time interval (the next year)
“t+1” is Nt+1
• Thus the relationship (growth or decline) of the
population is expressed Nt+1=λtNt
• λ describes the annual population growth rate (from one
year to next)
• If λ > 1, the population is growing, if λ < 1 the population
is declining, λ = 1 stable
• For some species, estimate λt = Nt+1/Nt
• More than just estimating change over time
Sources of Variation in
Population Growth
• Population growth λ can be influenced by
a number of factors that can influence
predictions of future population size
– Environmental stochasticity (random
fluctuations)
– Environmental catastrophes and bonanzas
(large perturbations)
– Demographic stochasticity (change variation
in vital rates)
Variation in Population Growth
• If population growth λ was the same every year,
prediction of population growth would be easy
• Spatial variation among populations is also
present
• Many factors both spatial and temporal result in
changes in population growth
• Increased variation in growth among years, even
if the long term average is the same has
detrimental effects
Variation in Population Growth
• One of the key results of population
models is that variation in population
growth reduces
• Even if the average growth rate (arithmetic
mean) is the same, increase variation
results in smaller (geometric mean) growth
rate
Arithmetic vs. Geometric
Mean in Growth
• Imagine a population where Nt+1=λtNt
where λt = {0.86 with prob ½, 1.16 with
prob ½
• Arithmetic mean of the two λ’s is 1.01
which would be the case for deterministic
(nonrandom) growth
• If you start with 100 individuals and the
population grows for 500 generations then
N500 = N0 (1.01)500 = 14,477
Arithmetic vs. Geometric
Mean in Growth
• But population growth is subject to stochasticity
or random variation
• Now imagine same population (100 individuals
growing for 500 generations) but grow rate
varies stochastically (randomly) either 1.16 or
0.86
• So with both growth rates about equally likely
(about 250 generations with high and with low
growth rates then population size after 500 is
N500 ~ N0 (1.16)250 x (0.86)250 = 54.8
• Adding variation to population growth λ usually
reduces population growth
Figure of Population Growth Rate
From Morris and Doak (2002)
Variation in Population
Growth Rate
• Addition of variation to population growth
rate will have additional consequences
• This will make future predictions of
population growth less certain
• It also means that there will be an
increasing probability of extinction (or also
of high population abundance)
Population Growth and Prediction
Populations of Clapper Rails
From Harding
et al. 2001
Other Sources of Variability
• Spatial variability in demographic rates also has
significant consequences for population survival
• Variation in vital rates usually vary from site to
site
• Degree of correlation among sites (spatiotemporal variability) substantially affects
outcome
• If a bad year in one population coincides with a
bad year in another population then this reduces
population viability
• If a bad year in one population coincides with
good years in other populations, this improves
viability
Observation Error or
Lack of Data
• Observation error
– Make measurements in better habitats
– Easier to find and mark healthiest plants (easier to
find) or less healthy animals (easier to catch)
– Difficulty finding/seeing organisms
– Estimates will be more variable thus more pessimistic
• Density dependence
– Negative density dependence (reduced growth rates
with increasing density)
– Positive density dependence (Allee effects,
decreased growth with decreased density)
Measuring Population Viability
• Very small populations (<100) are subject to
additional processes (inbreeding, demographic
stochasticity) that complicate simple population
projections
• Conservation biologist typically estimate time to
a “quasi-extinction” threshold
• Metrics often calculated
– Probability of quasi-extinction in a given time
– Probability of quasi-extinction ever occurring
– Mean time to extinction
Probability of Extinction
Viability Based
on
Population
Growth
• Growth rates may be more useful for populations
where short-term extinction probabilities are low
but population is vulnerable
• Atlantic right whales are currently at a population
size of a bit less than 150 and declining
• The probability of extinction in the next 100
years is nearly zero, but is almost a certainty
within 300 years
Viability Based on
Population Growth
• Managers must increase the population growth
rate above the current rate of λ = 0.976 to make
population viable
• Higher growth rates obviously reduce probability
of extinction (similar answers)
• Population growth is better estimated with
limited data
• Stochastic growth is influenced less by temporal
variability than is risk of extinction
Assumptions with
Simple PVA Models
• No density dependence
• No demographic stochasticity
• No trends or correlation in environmental
variation
• Environmental variation is moderate
• Census counts represent entire population
Demographic PVAs
• Particularly with long-lived organisms all
individuals are not equal
• Need to explicitly account for differences in
growth, survival and reproduction with age
• Use matrix population models to project future
population growth
• Based on survival, growth and reproduction of
different individuals in population
Demographic PVAs
• Conduct study using marked individuals
and measure growth, survival and
reproduction over several years
• Classify individuals into stages like size or
age (unknown for many species)
• Stages dependent on species (e.g. young
juvenile, old juvenile, young adult,
reproductive adult, old reproductive adult)
• Estimate vital rates for each stage
Matrix Population Model
Elasticity Analysis
• Elasticity analysis is a method determining the
“sensitivity” of population growth (λ) to scaled
changes in vital rates (growth, survival,
reproduction)
• The analysis looks at this sensitivity of growth to
change in each element in the matrix (for each
stage)
• Based on this, we can conclude which elements
(which stages and rates) will have the greatest
influence on population survival
Identifying Key
Life Stages
• Management actions can be determined based
on information about which life stages are most
important for population growth
• Crouse et al. (1987) and Crowder et al. (1994)
used PVAs to assist with management of
threatened logger head turtles in southeastern
U.S.
• Need to detemine which of two major threats to
logger head turtles is most important
– Trampling of eggs and hatchlings on beaches
– Drowning of adult turtles in fishing nets
Loggerhead Turtle PVA
From Crouse et al. 1987
Identifying Key
Life Stages
• They use PVAs on population data to measure
the contributions of different life stages to
population growth
• They found that reproductive adults were the
most important stage
• Efforts aimed at saving eggs and hatchlings
would not reverse population declines even if
they were 100% effective
• Putting TED (turtle excluder devices) in fishing
nets to prevent drowning would produce
recovery even if didn’t eliminate all mortality
Analyzing
Monitoring Data
• Gerber et al. (1999) used monitoring data for
eastern Northern Pacific Gray Whales
• They asked how many years of data would be
needed to determine if these whales should be
delisted (reach population target)
• Population increased to mid 1990s and was
delisted in 1994 but with no quantitative basis
• They found the delisting was warranted, but also
this could have been done several years earlier
Consequences of
Elasticity Analysis
• Determine which stages contribute most to
population growth
• Management can focus on most important
life stages
• Reserves can be created to accommodate
most important life stages for organisms
with complex life histories, migration