Assessing Population Viability

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Assessing Population Viability

• Applying estimates of population size to a
  conservation problem
• Two emphases projecting populations studying
  mechanisms that cause the decline (Graeme
  Caughley 1994)
• Declining population paradigm / small population
  paradigm
• Mechanistic studies have been under-emphasized
• Several methods for assessing viability

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Methods for Assessing Viability

• Estimate population growth rate (?, lambda)
• Trend Analysis population trajectory through
  time
• Matrix projection
• A better way to estimate ?
• A way to project populations
• WE ARE JUST SKIMMING THE SURFACE OF THESE METHODS
  TO GIVE YOU AN IDEA OF THE OPTIONS AVAILABLE. I
  DONT EXPECT A WORKING KNOWLEDGE OF PVAs

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Possible goals for a PVA

• Estimate chance of quasi-extinction, persistence
  or recovery or
• Assess alternate management strategies impacts on
  persistence likelihoods
• Assess external attributes and their impacts of
  persistence (fire, flooding, weather)
• Predict life history stages that have the most
  sensitivity with respect to persistence (and then
  which you should manage).

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Most studies have either a long time trend on few
populations or Few years on lots of populations.
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TREND ANALYSIS N(t1) ? Nt Estimate mean ?
and variance
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Method 1 Census Data

• Diffusion Approximation methods
• Simulation, using individual transitions as
  equally likely to occur and random draws of
  transitions

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A note on Quasi-extinction and density-dependence
Carrying capacity
Density dependence
Quasi-extinction threshold
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The relationship between ? and Long term
population size
Adding stochasticity adds variability
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Variation magnifies through time in the same way
that errors propagate and magnify upon themselves
In both growing and declining populations, a
projection will have an increasing likelihood of
extinction through time
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You can then estimate the likelihood of crossing
an extinction Threshold and plot this against
time as a measure of viability The likelihood
of persisting for a given period of time
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Matrix projection

• Stationary matrix
• ?
• Stochastic matrix projection
• Random elements
• Random matrices
• Random element and covariation among elements

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Matrix construction estimate the probability of
individuals in transition.
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Age Class Matrix
Size Class Matrix
Plants vs animals
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NOTE Not all elements ever filled in. AND you
also need some Population data from which to
begin
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MATRIX ALGEBRA --- can be used to (a) calculate 8
or (b) Project populations
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95 confidence
Mean projection
95 confidence
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Find a meaningful response variable Foliage area
Some real data Schulze and Carpenter
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Step 1 construct a transition probability
matrix NOTE problem with SEEDS Step 2 decide
how you would like to introduce
stochasticity -for now we will use the variance
around the transition probabilities
for each element
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Step 3 project population and record mean and
95 CI For runs through time. ---- type of
response to report time to x of runs hit
extinction and why that might not be the
best way to present info.
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More on Matrices

• Outcomes
• Population size through time
• Extinction Likelihood
• Quasi-extinction

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Small populations may have other problems that
drive them toward Extinction. Using a extinction
threshold suggests this, but results in A
complicated diagram
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One way to test sensitivity is to muck about with
a transition Probability in order to predict
response
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Another way to estimate sensitivity is with
partial derivatives Sensitivity analysis
examines the effect of small changes
in Individual elements on 8
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Adding stochasticity

• Error around matrix elements
• Randomly select a number for each element at each
  time step using the mean and variance and a
  normal distribution.
• Randomly select transition probabilities
  calculated from different years
• Calculate transition matrices for each year of
  the data, randomly choose years and select the
  matrix from that year

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Adding stochasticity

• Randomly choose an element, based on measurement,
  use covariance in element to all others in order
  to randomly select all the other elements based
  on deviation from mean for the 1st element
  selected

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Some words on utility

• Very data intensive, lots of assumptions
• Not likely to be done for many species
• Often we have to use surrogate species to
  estimate certain transitions

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Adding Space Metapopulations

• Levins 1970. Conceptual framework
• a population of populations may add stability to
  the entire population
• through extinction-recolonization process.
• 1980s Hanksi showed metapopulation dynamics
  in butterflies
• 1990s everyone with more than one population
  referred to having a metapopulation.

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Metapopulation a population of populations
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At any one time some are occupied, others empty
occupied
occupied
occupied
occupied
Empty
Empty
occupied
occupied
occupied
occupied
occupied
Empty
occupied
occupied
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Movement allows recolonization
occupied
occupied
occupied
occupied
Empty
Empty
occupied
occupied
occupied
occupied
occupied
Empty
occupied
occupied
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occupied
Empty
Resulting in increased overall persistence
Empty
Empty
occupied
occupied
Empty
occupied
occupied
Empty
occupied
occupied
occupied
occupied
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And so on.
occupied
Empty
occupied
occupied
occupied
occupied
occupied
occupied
Empty
occupied
Empty
occupied
Empty
occupied
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BUT
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More likely alternatives to metapopulations

• 1) Single large population with patchiness
• Movement between patches is so high that the
  populations function as a single population

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More likely alternatives to metapopulations

• 2) Isolated populations
• movement between patches is so unlikely that the
  populations are functionally isolated

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More likely alternatives to metapopulations

• 3) Source-sink or mainland-island populations
• When the dynamics of the system are driven by a
  single population whose growth rate is much
  higher than others.

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In a nutshell

• Patchiness alone does not
• indicate
• metapopulations

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Assessing Viability in metapopulations

• Requires first establishing that metapopulation
  dynamics are afoot.
• Then requires estimates of patch extinction rates
  and colonization rates.