# Population Viability Analysis _PVA_

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```					Population Viability
Analysis (PVA)
PVA
   A systematic examination of interacting factors
that place a population or species at risk of
extinction
 How  do we characterize risk?
 How do we examine interacting factors
(stochasticity,anthroprogenic, genetic, habitat)?
 What are the positives and negatives of this
approach?
Characterization of Risk
   Probabilities of Extinction/Persistence
 Extinction, management threshold, or quasi-extinction
 Time frame (ex. Probability that spotted owls will
persist for next 100 years is 0.30)
   Mean time to extinction
   Ex. If probability of persistence for 10 years (P10)
= 0.8, what is mean probability of persistence?
 Probability   of persistence for 1 year (P1) = 0.81/10 =
0.9779
 Mean probability of persistence = 1/-ln(0.9779) = 45
years
How?
 Rules of Thumb
 Count-Based
 Often   assuming a census
   Demographic Models
 Generally   matrix models
Count Based
   Census, Estimates of Abundance/Density
 Determinisitic
   E.g., Exponential/Logistic Models
 Stochastic
   Incorporating process variance
Deterministic vs Stochastic
   Geometric vs arithmetic
mean
   Stochastic change
   Prediction diverge over
time
   Ending distribution is
skewed
   Diverge from arithmetic
mean
   Center on geometric mean
for large n
   Still some can go extinct
Probability of Extinction and
Stochasticity
   Define
μ  = lnλG = mean
(arithmetic) lnλt-x + …
lnλ0 / t
   u > 0, λG >1, u < 0, λG
<1
   < u, higher probability
 σ2= variance of the
mean lnλG
   > σ2, more peaked
Example: Yellowstone Grizzlies

   Census - Assumed
   Density Independent
   Estimate μ and σ2
from count data:
Grizzly Extinction Probability
 Calculate visually from stochastic
projections:
 Or from μ and σ2
Assumptions
   Mean and variance of λ constant
 No density dependence
 No demographic stochasticity
 No environmental trends

 Uncorrelated environmental conditions
 Environmental variation is relative small
 Census is a census
Count Based Generalized
 Density Dependence
 Demographic Stochasticity
 Correlated Environments
 Catastrophes
 Bonanzas
Density Dependence in Small
Population
   Place cap on maximum size
 Population   may be small enough to remain at
risk of extinction even at maximum size
   Allow higher growth rates at smaller sizes
 AlleleEffects – positive density dependence
 Inbreeding depression
Demographic Stochasticity
 Need variances in rates to incorporate
 Raise quasi-extinction threshold to
minimize effects
 Magnified effects of environmental
stochastcity with demographic
stochasticity
Environmental Autocorrelation
   Positive autocorrelation
 Increasesextinction risk in density-
independent models
 Complicated for Density-dependent models

   Negative autocorrelation rare or non-
existent
Catastrophes and Bonanzas
 Rare events that are difficult to incorporate
 But, … can have the greatest effect
Components of Variance
Analysis
   See notes and
   Gould, W. R. & Nichols,
J. D. (1998). Estimation
of temporal variability of
survival in animal
populations. Ecology
79:2531–2538

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 views: 3 posted: 2/1/2012 language: English pages: 21