A. Endangered Species and Population Viability
1. Desire to bring science
to recovery process
2. Many attempts to make
rigid numbers about targets for recovery, including these early
recommendations:
-- 50/500 rule
-- 99% chance
of persistence for at least 1000 yrs
A. Goal: To use ecological models to forecast trends in future
population size
B. Structure: There is not one standard approach to conduct a PVA
- let the data dictate the PVA
approach
- keep the model as simple as
possible
- models can
easily
get very complex
C. Data needs: depends on model
1. For count based data,
>10 yrs
2. For stochastic
demographic model, 4 yrs
3. For deterministic
demographic model, 2 yrs
4. For spatial
(metapopulation) PVA, 20 subpopulations
D. Uses of PVA
1. Compare risks in two or
more populations
2. Analyze or synthesize
monitoring data
3. Identify key life stages
for management
4. Determine number of
populations to protect
Problem:
Contrast between the dire need for PVA and the
scarcity
of data in conservation – modeling realistic population changes could
involve
many factors
E. PVA emphasizes variability, not just mean!
1. Stochasticity, in general, increases
extinction
risk
-- geometric v. arithmetic mean
2. Variability causes projected population
sizes
to rapidly diverge
-- California Clapper Rail example
3. Catastrophes and bonanzas in particular are
difficult
to quantify
4. Contrasting effects of negative density
dependence
5. Positive density-dependence can increase
population
risk
6. Other factors (ie, genetic, spatial) can
greatly
increase uncertainty in PVA
F. What measure to quantify extinction risk?
1. Do not quantify risk of utter extinction -
set some higher threshold
2. Measures of population size generally not
sufficient
3. Measures of population growth can be useful
4. What measure to use to quantify extinction
risk?
-- the ultimate probability
of extinction at any future time - asymptote of Cumulative Distribution
Function (CDF)
-- mean (calculated)
-- median (50th percentile on CDF)
-- mode (peak on Probability
Distribution Function (PDF))
-- the probability of extinction
at some future time (CDF)
5. Probabilities of extinction over certain
time horizons are the most useful and robust extinction risk estimates
To get these, need an estimate of probabilities of extinction
II. PVA with count data
A. Overview
1. Start with simplest assumptions
- Mean and variance of population
growth
rate remain constant
- Environmental conditions uncorrelated
- Environmental variation is small
- No observer error
2. Characteristics of density-independence
- Probability that population
will
be some size at any future time described by lognormal distribution
(thus,
log(N) is normally distributed)
- Over time, mean population size
will
change in relation to lambda, but variance will grow
- Characterize population growth
by
log of the geometric growth rate (mu)
- Variance parameter for log
growth
rates - sigma squared
Note: Do
not quantify risk of utter extinction - set
some
higher threshold
- Assuming a diffusion
process, can generate PDF (and thus CDF) with an inverse Gaussian
distribution that requires parameters μ, σ2, and the difference between
population size and the extinction threshold
B. Practical methods for making calculations of mu and sigma square
1. Because variance changes over time and time
interval
may vary, need to normalize with regard to time interval
- divide log(Nt+1/Nt) by square
root
of the time interval
2. Regress square root time interval against
normalized
population change (forced through origin)
3. Slope is mu and error mean square is the
estimate
of sigma square
4. Confidence intervals for mu calculated with SE
and
two-tailed Students t
5. Confidence intervals for sigma square
calculated
using chi-square distribution
6. Create PDF, CDF, and CI using MatLab
C. Keep in mind assumptions (no temporal
autocorrelation,
extreme
events, or changes in mu or sigma square over time)
D. Examples of how PVA can be used
E. Tips on using PVA:
1. Avoid conducting formal PVA when data are too sparse
2. Present confidence intervals
3. Compare relative rather than absolute changes
4. Do not project population viability too far into the future
5. Start with simple models: let the data choose the model