Transcript PPT

Announcements
• HW Addendum for CONS670
• Reading assignment for BSCI363
Population Density (Ln)
Mean r = 0, P(extinction) = ?
pop “a”
pop “b”
pop “e”
pop “g”
pop “c”
pop “d”
pop “h”
TIME
pop “f”
General Predictors of Extinction
+
-
Population Growth
Current population size
Population Size
General Predictors of Extinction
• Carrying capacity / population size.
• Maximum growth rate.
• Variation in growth rate
– Demographic stochasticity
– Environmental stochasticity
– Genetic stochasticity
Variation in B&D: Demographic
Stochasticity
• “Transparent” in VORTEX
• Probabilistic nature of births and deaths,
males and females
• Function of
– Birth and death rates
• Fecundity = 0.34?
– Sex ratio
Variation in B&D: Demographic
Stochasticity
Monogamy
1 male
1 female
Polyandry
> 1 male
1 female
Polygyny
1 male
> 1 female
> 1 male
> 1 female
Polygynandry
Polygamy
“random breeding”
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”
Yearly Variation in Fecundity
frequency
X= 34%
s.d.
s.d.
s.d.
s.d.
14
24
34
44
% of females producing offspring
~68%
~95%
54
Calculating S.D. from Data (> 5 yrs.)
A
B
1
Year
Fecundity (%)
2
1994
24
3
1995
34
4
1996
14
5
1997
44
6
1998
54
7
SD
= STDEV(b2:b6)
Calculating S.D. from Data (> 5 yrs.)
A
B
1 Year
bx
C
n

i 1
2 1994
24
(34-24)^2
3 1995
34
(34-34)^2
4 1996
14
(34-14)^2
5 1997
44
(34-44)^2
6 1998
54
(34-54)^2
X  X 
2
i
n 1
Sqrt(Sum(c2:c6)/(5-1))
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.
• Where mean value (e.g. fecundity) =
34%
• “highly tolerant of EV”
– let SD = 34%*.05
• “very vulnerable to EV”
– let SD = 34%*.50
• “intermediate tolerance”
– let SD = 34%*.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
• 1980: 445 seals out of
~10,000 died.
• “Few” seals reproduce
J. R. Geraci et al., Science 215, 1129-1131 (1982).
Catastrophes: Harbor Seals
• Disease outbreaks in
1931, 1957, 1964, and
1980
• 445 seals out of
~10,000 died.
• “Few” seals reproduce
• Probability of catastrophe:
– 26, 12, 14 years between
outbreaks
– Average time between
outbreaks = 17 years.
– 1 every 17 years or 6 every
100 years.
Loss (e.g., % surviving)
– 9,555 / 10,000 ~ 95%
– Reproduction = ?
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)
Variation in B&D: Genetic
Stochasticity
Aa
x
A
a
A a
AA Aa
Aa aa
Aa
Where a is deleterious
Homozygous recessive is lethal
(Recessive Allele Model)
Presence of “a” allele decreases fitness
Reduced fitness = sum of lethal equivalents
(Heterosis Model)