The Hookers Sea Lion

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Predicting Extinction

• The Hookers Sea Lion

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Nature of extinction

• The taxonomic group of interest has no members
  (in the wild or captivity?)
• caused by an average negative rate of increase
  for a long period of time

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Causes of extinction

• Competition predation
• Climate Change
• Habitat loss
• Exotic species introductions
• Disease
• Other catastrophic event
• Exploitation

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Modeling extinction

• Random walk with negative or close to negative
  rates of increase

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Key parameters

• Average rate of increase
• Process error
• Starting population size
• Pseudo-extinction threshold
• Often ignored - red noise autocorrelation of
  process errors - show general model!

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What is missing

• Density dependence, especially decreasing rates
  of increase at very low densities
• Catastrophic events

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Hookers Sea Lion(Phocarctos hookeri)

• Found only in NZ
• Main breeding sites are in Auckland Islands
• Historical range may have included main islands
• depleted to near extinction in 18th and 19th
  centuries

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Concerns

• Listed as vulnerable - then upgraded to
  threatened, based on the lack of breeding sites
  at places other than Auckland Islands
• Population size estimated at 14,000 animals
• about 80 per year killed as by-catch in squid
  fishery
• NZ DOC wants to limit by-catch by closure of
  squid fishery

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Goals

• Allow population to increase so that colonization
  at a new site takes place
• Best way to achieve this is by letting population
  reach 90 of K
• Contrast with western stock of Stellers Sea Lion

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Our model

• Spatially explicit 8 populations
• Dispersal between sites
• Allowed for depensation
• Allowed for catastrophic events
• Used existing data in integrated Bayesian
  framework

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The problem

• Estimate impacts of squid fishery by-catch on two
  major indicators
• Probability of extinction
• Probability of establishing new breeding colonies

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Key components of approach

• Model to estimate parameters from available data
• Forward projections to calculate impacts of
  by-catch and catastrophies
• Literature review to determine intensity and
  probability of catastrophies
• Literature review to determine what is known
  about population dynamics of otariids

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Data available

• Irregular pup counts at some of the locations

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Key elements of model

• Age structured
• 8 possible breeding sites
• model dispersal between sites
• allow for depensation
• allow for catastrophic events

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Why age structure?

• The important parameter is rate of increase - a
  total numbers model would be appropriate
• But -- the data are pup counts - keeping track of
  age structure lets us predict observed pups

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Key parameters

• Pups per female
• juvenile survival
• adult survival
• only one aggregate rate of increase is really
  estimable!

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Density dependence

• Wanted flexible model to allow for different
  shapes in production curve

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Why spatial model?

• Additional breeding sites may make population
  less vulnerable to catastrophic events
• Data come in different years from different
  sites, thus we cant pool Auckland Islands data
  into one area

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Alternative model of dispersal

• From Barb Taylor - build up at beaches until
  density is high - then large numbers move to new
  site - usually a few miles away
• This could be modeled, but obviously would be
  unlikely to move animals outside the Auckland
  Islands
• Might want to make the probability of dispersal a
  higher power of density

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Key assumptions in dispersal model

• The proportion that disperse increases with
  density so that when density doubles the number
  dispersing goes up four times
• Probability of dispersal from one area to another
  decreases with distance between sites

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Why depensation?

• We need to consider the possibility that rates of
  increase decline at low densities, this is a
  common hypothesis for causes of extinction
• We used an exponential model but do not believe
  the particular shape is important
• There is information about depensation from the
  data on New Zealand sea lions, and in the
  historical record

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Model derivation

• Assumes a random mating model, that the
  probability a female goes unmated is the
  probability of her not encountering a mate, and
  this encounter rate is random.

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Our likelihood

• Chose normal likelihood with different s.d. for
  each population
• s.d. was chosen based on a CV of 0.5 except for
  the three populations with 1 or 2 animals counted
• For all except Sandy the empirical CV is about 0.5

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Why catastrophic events

• Most of the concern about threat to NZ sea lions
  relates to the impact of catastrophic events
• If we want to model extinction risk or changes in
  abundance we have to model catastrophic events

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Our model

• The probability of a catastrophic event is the
  same in all years
• All individuals of all ages are equally affected
• Two choices - all areas affected equally, or
  Auckland Islands together, all others independent

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Other models

• The intensity or probability of a catastrophic
  event could be density dependent (disease and
  contact rates)
• Only breeding (or non breeding) animals are
  affected

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Why look at only big events

• If we want to consider small events - i.e. pup
  die offs, 20 mortalities, then we would need to
  consider the possibility that these have occurred
  in the last 30-40 years, and therefore the
  observed rates of increase reflect small events
• This is technically hard to do and should
  automatically be incorporated in observed rates
  of increase

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Choices in the meta analysis of catastrophies

• Two types of major catastrophic events in
  otariids - the long slow declines of Western
  Stellers and South American sea lions, and the
  El Nino type declines in the eastern Pacific.
• We found 7 such events with 50 or greater
  mortality

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What denominator to use

• If we use only years where current scientific
  methods for pup counts were used, we obtain a
  denominator of 273 and a probability of 2.5.
• This obviously greatly overestimates the
  probability,

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How likely are we to have observed a massive
mortality

• Clearly none has happened for at least 30 years
  with NZ sea lion - yet we used only 2 years data
  for out 2.5 calculation
• If we use the length of the historical record we
  obtain 0.28
• This is too low
• We chose 1 effectively saying there is a 25
  chance of having observed a massive mortality at
  any time in the historical record

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Depensation

• Reviewed the entire published literature for all
  otariids (sea lions and fur seals)
• found that numerous populations had been driven
  low enough to be thought extinct by exploitation
• had all recovered from such low levels
• other analysis in progress

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Catastrophic events

• Considered only events of 50 or greater
  mortality on reproductive individuals
• Seven such events what denominator to use
• If we assume only when populations closely
  monitored we get 2 probability
• Our best estimate is 1 probability

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General conclusions

• Risk of extinction is quite low, IUCN criterion
  is 10 probability in 100 years, we are 1/20th of
  that
• Highly unlikely that new breeding colonies will
  be formed in next 20 years
• By-catch has very small impact on population,
  dynamics dominated by catastrophes

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Model improvements

• Add process error other than catastrophes
• Likelihood for low counts
• Accounting for small populations
• Better quantification of priors -- especially for
  depensation and catastrophes