Density dependence 08

Density dependence 08 - Density dependent count PVA Jan. 28...

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    Density dependent count  PVA Jan. 28 2008
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    Density dependence & extinction time Ultimate extinction becomes certain Ceiling model : like density independent but  growth stops above  K Mean extinction time given by: (initial population size is  K ) How much benefit do we get from increasing  carrying capacity? 2 2 / 2 2 2 1 1 2 / log 2 / T K K μ σ μ σ = - -
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    Extinction time & carrying  capacity σ 2  = 0.1 μ  = 0.1 N x  = 1 N C  =  K
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  checkerspot  butterfly Endangered species restricted to serpentine  outcrops in SF Bay area Extensively studied for ~30 yr JRH population size 0 1000 2000 3000 4000 5000 6000 7000 8000 1960 1965 1970 1975 1980 1985 Year # females JRH density dependence -3 -2 -1 0 1 2 3 0 1000 2000 3000 4000 5000 6000 7000 8000 N(t) r(t)
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    More general density dependence For other models, must use simulation to  estimate mean extinction time For  all  models, must use simulation to estimate  CDF Data analysis issues: Which model should we use? What parameter values do we use? Reverse order: must have best fit parameter  values for each model before comparing them
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    Parameter estimation Define: f  is the density dependence function is the parameter(s) of the model Use nonlinear minimization to find value of theta that  minimizes sum of squared residuals:
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Density dependence 08 - Density dependent count PVA Jan. 28...

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