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• 50-100 individuals

• Environmental stochasticity• 1000-10,000 to buffer against

• Natural catastrophes• > 1 population

• Genetic stochasticity• 50- 500

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– Nt+1 = Nt+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)

0.84

0.84

0.84

0.26 0.07

0.21

0.34

x lx bx

0

1

2

3

... 20

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

Pop

ula

tion

Den

sity

(L

n)

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”

freq

uen

cy

X= 34%

% of females producing offspring

Yearly Variation in Fecundity

14 24 34 44 54

s.d.s.d.

~68%

~95%

s.d.s.d.

A B

1 Year Fecundity (%)

2 1994 24

3 1995 34

4 1996 14

5 1997 44

6 1998 54

7 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 +/- 2.25 SD• For N ~ 100, assume range defines +/- 2.5 SD• For N ~ 200, assume range defines +/- 2.75 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 1980

• 445 seals out of 600 (part of a larger population ~10,000) died.

• “Few” seals reproduce

J. R. Geraci et al., Science 215, 1129-1131 (1982).

Catastrophes: More Info

• Mangel, M., and C. Tier. 1994. Four facts every conservation biologist should know about persistence. Ecology 75:607-614.– General background

• Young, T. P. 1994. Natural die-offs of large mammals: implications for conservation. Conservation Biology 8:410-418.– Possible reference or starting point for term-paper

• Access through JSTOR (www.jstor.org)