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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

Predicting Extinction

Causes of extinction

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

Predicting Extinction

Modeling extinction

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

Predicting Extinction

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!

Predicting Extinction

What is missing

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

Our model

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

Predicting Extinction

The problem

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

Predicting Extinction

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

Predicting Extinction

Key elements of model

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

Predicting Extinction

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

Predicting Extinction

Key parameters

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

Predicting Extinction

Density dependence

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

Predicting Extinction

Why spatial model?

- Additional breeding sites may make population less vulnerable to catastrophic events
- Data come in different years from different sites, thus we can’t “pool” Auckland Islands data into one area

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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.

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

Choices in the meta analysis of catastrophies

- Two types of major catastrophic events in otariids - the long slow declines of Western Steller’s 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

Predicting Extinction

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,

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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

Predicting Extinction

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