1 how small can a population get before inbreeding becomes intolerable? if f = 1 and n e = 4 m f 2n...
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1
How small can a population get before inbreeding becomes intolerable?
If F = 1 and Ne = 4 M F 2Ne M + F
Then F = 1 and F = 1 + 1 2 4 M F 8F 8M
M + F
60a
Important!
Formulas first:
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How small can a population get before inbreeding becomes intolerable?
F = 1 + 1 8F 8M
Research on domestic farm animals:
natural selection for performance can balance inbreeding
depression if the ΔF is no more than 1% per generation.
So, F = 0.01 is a tolerable level of inbreeding
60a
3
How small can a population get before inbreeding becomes intolerable?
F = 1 + 1 8F 8M
If F = 0.01 is a tolerable level of inbreeding, then
.01 = 1 + 1 so F = 25 and M = 25 8F 8M or, Ne = 50
60a
Magic number!
4
Num
ber
of f
emal
es
Number of males
15.01 tolerance
.005 tolerance
What happens to the ‘magic number’ when sex ratios are unequal?
25
1 1 8Nm 8Nf
+F =
Conclusion:15 = smallest number of effective individuals of one sex
60
25
5
Population bottlenecks
Pop
ulat
ion
size
Time
bottleneck
H = 1 - 1 = expected proportion of Ho retained after a2Ne 1-generation bottleneck
Ht = Ho 1 - 1 t = proportion of Ho retained t generations after 2Ne a bottleneck
if Ne = 4 at t=0, then Ht=1 = 1 - 1 = 7 i.e. 1/8 of original H 2 x 4 8 was lost in 1
generation 61A
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The effect of bottlenecks on H
# ofindividuals
Generations
1 10 100
2 .75 .06 .00
4 .88 .26 .00
10 .95 .60 .01
25 .98 .82 .13
50 .99 .90 .37
100 1.00 .95 .61
Proportion of original heterozygosity remaining in small populations
61-1
7
Probability of retaining a rare allele after a bottleneck of size N for a single generation
Population size (Ne)250
q = .05
q = .01
q = .10
Pro
babi
lity
of
rete
ntio
n
1.0
0
61-2
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Conclusions: Effects of Inbreeding and Bottlenecks
H P--------------------- -------------------
Bottleneck: decreases by 1/2Ne LARGE decreasewith reproduction especially of rare alleles
Inbreeding: LARGE decrease no change
65
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Effects of a genetic bottleneck in a plant:
Lakeside daisy (Hymenoxys acaulis)- only one population survived agriculturaldevelopment
- self-incompatibility
- requires mates of a different mating type
-but alleles for only one mating type survivedthe bottleneck…..
10
Founder Effect
Wild population zoo
Speke’sgazelle
Founders to zoo in 1970s: 1 male, 3 females N = 4, but Ne = 2
Initial severe inbreeding
In 1982, N = 29
Inbreeding depression eliminated. Escaped F - vortex?
65A
(Founders)
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Contribution of 16 founders to the captive Guam Rail population
Founders
% F
oun
der
con
trib
uti
on
0
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 31 32 33 36 98
10
5
15
65e
Expected
1/16 = .0625
12http://www.ultimateungulate.com/gazellespeke.html
Speke’s gazelle
13http://www.ultimateungulate.com/okapi.html
Okapi
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Goeldi's monkey and Okapi
• 40% loss of genetic diversity in captive populations due to unequal founder contribution
Drosophila on Hawaiian Islands
• 95 of 100 species are endemic to only one island or volcano (results of migration of single, fertilized “eves”)
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Population Management: Founder Effect
Wild population founders
65A
Problem: Founding event--> forced inbreeding --> inbreeding depression
Best Solution: MAXIMIZE GROWTH OF THE POPULATION A.S.A.P.!!
16
What is the minimum Nenecessary to maintain
evolutionary potential???
500
The other magic number
Selection balances Drift…..Maybe!!!!
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III.The Biology of Small Populations1. Population Dynamics of Small Populations2. Genetics3. Population Viability Assessment
IV. The Ecology of Conservation and Extinction
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Minimum Viable Population
• First stab: 50 / 500 rule.
• John James Audubon – the first PVA
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Mauritian Kestrel
1970’s: Rarest bird in the world!
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Triage
• Triage: Sorting the casualties of war into those too badly wounded to recover, those who can survive without help, and focusing on the remainder.
21
Triage Conservation Biology
• “We might abandon the Mauritius kestrel to its all-but-inevitable fate, and utilize the funds to proffer stronger support for any of the hundreds of threatened bird species that are more likely to survive” - Norman Myers, The Sinking Ark
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Hopeless Cases?
There are no hopeless cases, only people without hope and expensive ones – Michael Soulé
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But . . .
• The Mauritius kestrel was never exceptionally common
• The fact still remains that we have limited resources to allocate to many species– 10 million $ to rent a Panda