Announcements Error in Term Paper Assignment –Originally: Would... a 25% reduction in carrying capacity... –Corrected: Would... a 25% increase in carrying capacity... Homework 3 Assigned

Extinction Risk as a Function Density Demographic stochasticity individuals Environmental stochasticity ,000 to buffer against Natural catastrophes > 1 population Genetic stochasticity

Spotted Owl Recovery How many breeding pairs are necessary? What management manipulation is most likely to prevent extinction? What stages of the life-cycle have the largest impact on population dynamics?

“Minimum Viable Population” (MVP) How large must a population be for it to have a reasonable chance of survival for a reasonably long period of time? –Reasonable chance often taken as 95%. –Reasonably long period, 100 years.

Population Viability Analysis (PVA) The science of determining the probability that a population will persist for a given time. We will use VORTEX

PVA as Population Ecology Applied Model –N t+1 = N t +B-D+I-E –B&D may be influenced by genetic factors –I&E Closed population vs. metapopulation Differences –Focal species –Implications

Stochastic vs. Deterministic Models B&D fixed –Deterministic models allow us to identify population trajectory and “critical” life-history stages. B&D variable –We cannot predict population size with certainty. We can only specify the probability of particular outcomes. –Stochastic models allow us evaluate the probability of extinction.

Deterministic Model for Spotted Owls Hatchlings Adults (age 3-20) Juveniles (age 1) Sub-Adults (age 2)

xlxlx bxbx Life Table: Spotted Owl

Management Plan: Spotted Owl Double juvenile survivorship Increase adult survivorship by 10% Double adult fecundity

“Sensitivity Analysis” Click here for Excel file

What About Extinction r is either greater than or less than 0. Risk of extinction is independent of population size. Fecundity of adult females = 0.34 exactly every single year.

pop “a” pop “b” pop “e” pop “g” pop “c” pop “d” pop “f”pop “h” TIME Population Density (Ln) Mean r = 0, P(extinction) = ?

Variation in B&D: EV Fecundity of adult spotted owls = 0.34 In a “normal” year: 34% of adult females have 1 female offspring. In a “bad” year, EV results in decreased r: e.g., births = 34% - “x” In a “good” year, EV results in increased r: e.g., births = 34% + “x”

frequency X= 34% % of females producing offspring Yearly Variation in Fecundity s.d. ~68% ~95% s.d.

AB 1 YearFecundity (%) SD= STDEV(a2..a6) Calculating S.D. from Data (> 5 yrs.)

Calculating S.D. From Data (Range) Average fecundity =.34 (range.14 –.54) Calculate S.D., based on years / data points For N ~ 10, assume range defines +/- 1.5 SD. For N ~ 25, assume range defines +/- 2SD For N ~ 50, assume range defines +/ SD For N ~ 100, assume range defines +/- 2.5 SD For N ~ 200, assume range defines +/ SD For N ~ 300, assume range defines +/- 3 SD

“Last Ditch” Estimate of S.D. For example where mean value (e.g. fecundity) = 34% “highly tolerant of EV” –let SD = 34%*.05 “very vulnerable to EV” –let SD = 35%*.50 “intermediate tolerance” –let SD = 35%*.25

Variation in B&D: Catastrophes Defined by VORTEX as episodic effects that occasionally depress survival or reproduction. Types (up to 25, start with 1) Independent causes of mass mortality. Probability based on data (# per 100 years). Loss due to catastrophe (= % surviving) 0 = no survivors. 1 = no effect.

Catastrophes: Harbor Seals Disease outbreaks in 1931, 1957, 1964, and seals out of 600 (part of a larger population ~10,000) died. “Few” seals reproduce J. R. Geraci et al., Science 215, (1982).

Catastrophes: More Info Mangel, M., and C. Tier Four facts every conservation biologist should know about persistence. Ecology 75: –General background Young, T. P Natural die-offs of large mammals: implications for conservation. Conservation Biology 8: –Possible reference or starting point for term-paper Access through JSTOR (