Demographic PVA in a nutshell

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Demographic PVA in a nutshell

• Create life-cycle graph
• Convert it to a transition matrix
• Estimate parameters for year-specific (if
  available) and average matrices
• For average matrix
• Calculate l1
• Calculate CI of l1
• Calculate sensitivities of l1 to vital rates

• If multiple years of data
• Calculate log lS
• Use simulations to estimate extinction risk
• Use sensitivity analysis of l1 to guide
  explorations of the effects of changing various
  vital rates on extinction risk
• If population is small
• Create models with demographic stochasticity
  (with or without ES)

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If you find yourself doing a lot of demographic
analysis

• Learn Matlab or R
• Get Hal Caswells book
• Caswell, H. 2001. Matrix Population Models
  Construction, Analysis, and Interpretation.
  Sinauer Press, 722 pp.

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Terminology for spatial PVA

• Site discrete patch of habitat that has some
  potential to maintain the species
• Local Population group of individuals living at
  a site
• Global (Multi-Site) Population individuals
  living at all sites
• Metapopulation multi-site population
  characterized by frequent local extinction and
  recolonization

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Endpoints

• Probability of global extinction
• Importance of given population for global
  persistence
• Value of increasing or maintaining dispersal
  between sites (e.g. through corridors)

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Scenarios

• Independent populations
• Mainland-island
• One highly viable site
• Other sites depend on immigration from mainland
  site
• Archipelago
• All sites with moderate viability, some dispersal
• Metapopulation
• Local extinction frequent
• Recolonization by dispersers frequent

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No dispersal

• If populations are independent then total
  extinction probability is product of local
  extinction probabilities
• Positive spatial correlation in environmental
  variables will increase overall extinction risk

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Low dispersal

• Local population dynamics qualitatively unchanged
• Extinct sites can be recolonized
• Inbreeding effects reduced

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High dispersal

• Substantial effect on local population dynamics
• Small local populations can be rescued
• Otherwise unviable local populations can be
  maintained (source-sink dynamics)
• Leads to spatial correlation in population size

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Data requirements

• Population size or demography at each site
• What do we assume for sites where we dont have
  data?
• Spatial correlations in environmental variables
• Negative correlations different habitat types?
• Positive correlations environmental drivers,
  tend to decline with distance
• Dispersal rates among sites
• Factors influencing emigration and immigration
• Dispersal mortality
• Behavior in matrix (non-habitat)
• Connection probability tends to decline with
  distance

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Quantifying environmental correlation

• Correlation in population growth rates
• Correlation in vital rates
• Correlation in weather variables
• Spatial extent of catastrophic events

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Clapper rail in SF Bay
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Vital rate correlations
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Rainfall correlations
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Clapper rail viability no dispersal
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Global viability depends on Mowry
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Quantifying dispersal

• Mark-recapture data
• Examine distribution of distance moved
• Behavioral observations
• Movement models (e.g. random walk) allow
  extrapolation from short-term measurements
• Genetic data
• Decline in genetic similarity with distance

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California gnatcatcher dispersal
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Clapper rail with dispersal
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Which grizzly pops are most important for
persistence?
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Multi-site demographic PVA (no dispersal)
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Multi-site demographic PVA (juvenile
dispersal)
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Spatial PVA in practice

• Dont have demographic or count data from all
  sites
• Dont have good estimates of dispersal
• Dont have quantitative estimates of spatial
  correlation
• Do know something about location, size, and
  relative quality of the sites
• For a really good example, see
• Akçakaya, HR, JL Atwood. 1997. A habitat-based
  metapopulation model of the California
  Gnatcatcher. Conservation Biology 11422434.
• http//www.blackwell-synergy.com/links/doi/10.1046
  2Fj.1523-1739.1997.96164.x

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Now for something completely different

• Suppose we know where all the sites of potential
  habitat are
• Its relatively easy to collect presence/absence
  data (at least for non-cryptic species)
• With multiple years of this, we can create a
  patch-based metapopulation model
• Focus on models by Illka Hanski

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Incidence function model

• For each patch, need to know area, distance to
  all other patches
• Extinction and colonization are patch specific
• Extinction depends on patch area

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Colonization

• Colonization probability is saturating function
  of number of immigrants
• Immigrants are more likely to come from large,
  close populations

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Probability of occupancy (incidence function)

• At equilibrium, so some
  algebra reveals

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Parameter estimation

• Data consists of annual surveys of presence or
  absence of species in every habitat patch
• Single survey fit incidence function to observed
  occupancy using nonlinear logistic regression
• Multiple surveys fit extinction colonization
  functions to observed extinctions colonizations
  using nonlinear logistic regression

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Simulating the metapopulation

• For each patch, calculate Ei and Ci(t)
• For each occupied patch, draw random number
  (uniform on 0,1) to compare with Ei
• If extinction occurs, draw another random number
  to compare with Ci(t) rescue effect
• For each unoccupied patch, draw random number to
  compare with Ci(t)
• Update patch status

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Glanville fritillary metapopulation
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Habitat loss metapopulation extinction