1 how small can a population get before inbreeding becomes intolerable? if f = 1 and n e = 4 m f 2n...

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:

2

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

6

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

8

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

9

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)

11

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

14

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”)

15

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!!!!

17

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

19

Mauritian Kestrel

1970’s: Rarest bird in the world!

20

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

22

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