announcements error in term paper assignment –originally: would... a 25% reduction in carrying...
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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
Management Plan: Spotted Owl
• Double juvenile survivorship
• Increase adult survivorship by 10%
• Double adult fecundity
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)