When a population is fragmented, different

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When a population is fragmented,
different fragments will have different initial
allele frequencies by chance. The extent of
diversification in allele frequencies can be
measured as variance in allele freq. as ?p2
pq/2Ne Thus, there will be greater variance
larger differentiation of allele frequencies
among small fragments.
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Additionally, on average, fragmented
popualtions have reduced heterozygosity and
increased variance in heterozygosity across loci
within populations. The average reduction in
heterozygosity due to sampling from the base
population is 1/2Ne. The initial reduction is
minor unless the population fragments are very
small (lt 10).
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As heterozygosity is lost within fragments
allele frequencies drift among fragments,
there is a deficiency of heterozygotes when
compared to HWE for the entire population and
this is known as the Wahlund Effect.
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Sometimes population substructuring is not
obvious, and as a result, a sample may consist
of a group of heterogeneous subsamples from a
population. For example, subpopulations may be
separated by subtle physical or ecological
barriers that limit movement between
groups. When these subpopulations are lumped
together and if there are differences in allele
frequencies among these subpopulations, there
will be a deficiency of heterozygotes and an
excess of homozygotes which is a Wahlund Effect.
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With increasing fragmentation, population
size within each fragment becomes smaller
and differentiation among fragments
increases. Inbreeding and inbreeding depression
will be more rapid in smaller than larger
fragments as will genetic drift and loss of
genetic diversity.
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Measuring Population Fragmentation
F-statistics Differentiation among fragments or
sub-populations is directly related to the
inbreeding coefficients within and among
sub-populations or fragments. Using inbreeding
coefficients, Sewall Wright described the
distribution of genetic diversity within and
among population fragments. He partitioned
inbreeding of individuals (I) in the total (T)
populations (FIT) into that due to
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Inbreeding of individuals relative to
their sub-population (FIS) Inbreeding due to
differentiation among sub-populations, relative
to the total population (FST). More
specifically, FIS is the probability that
two alleles in an individual are identical by
descent. This is the inbreeding coefficient (F)
averaged across all individuals from all
population fragments.
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FST, the fixation index, is the effect of
the population sub-division on inbreeding. FST
probability that two alleles drawn at random from
a single population fragment (either from
different individuals or the same individual) are
identical by descent. With high rates of gene
flow among fragments, this probability is low.
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With low rates of gene flow among
fragments, populations diverge and become inbred
and FST increases. F-statistics are used to
understand factors involved in causing a
population to deviate from Hardy-Weinberg
expectations.
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Deviations from HWE has 2 components Deviations
due to factors within subpopulations Deviations
due to factors among subpopulations If the
deviations result from excess of HOMOZYGOTES,
there may be selection, inbreeding, or further
population subdivision. If deviations result
from excess of HETEROZYGOTES, there may be
overdominant selection or outbreeding.
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Terms Equations for F-statistics F fixation
index and is a measure of how much the observed
heterozygosity deviates from HWE F (He -
Ho)/He HI observed heterozygosity over ALL
subpopulations. HI (?Hi)/k where Hi is the
observed H of the ith supopulation and k
number of subpopulations sampled.
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HS Average expected heterozygosity within each
subpopulation. HS (?HIs)/k Where HIs is
the expected H within the ith subpopulation and
is equal to 1 - ?xi2 where xi2 is the frequency
of each allele.
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HT Expected heterozygosity within the
total population. HT 1 - ?xi2 where xi2 is
the frequency of each allele averaged over ALL
subpopulations. FIT measures the overall
deviations from HWE taking into account factors
acting within subpopulations and population
subdivision.
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FIT (HT - HI)/HT and ranges from - 1 to
1 because factors acting within
subpopulations can either increase or decrease
Ho relative to HWE. Large negative values
indicate overdominance selection or outbreeding
(Ho gt He). Large positive values indicate
inbreeding or genetic differentiation among
subpopulations (Ho lt He).
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FIS measures deviations from HWE
within subpopulations taking into account only
those factors acting within subpopulations FIS
(HS - HI)/HS and ranges from -1 to
1 Positive FIS values indicate inbreeding
or mating occurring among closely related
individuals more often than expected
under random mating. Individuals will possess
a large proportion of the same alleles due to
common ancestry.
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This leads to a reduction in Ho relative to
HWE (Ho lt He). Negative FIS suggests
outbreeding or mating mating occurring among
individuals having different genotypes more often
than expected under random mating (Ho gt
He). However, while large negative and positive
values of FIS indicate non-random mating, the
interpretation of FIS is the same as FIT.
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Thus, there is the possibility of
overdominant selection or further subdivision
(Wahlund Effect). If you knowingly lump
different subpopulation into one, FIS will be
positive not because of inbreeding but because of
population differentiation. An understanding of
the populations natural history can address the
likelihood of this possibility.
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FST measures the degree of differentiation among
subpopulations -- possibly due to
population subdivision. FST (HT - HS)/HT and
ranges from 0 to 1. FST estimates this
differentiation by comparing He within
subpopulations to He in the total population. FST
will always be positive because He
in subpopulations can never be greater than He
in the total population.
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As a general rule of thumb, values of FST that
are statistically different from 0 0.05 --gt
0.15 moderate genetic differentiation. 0.15
--gt 0.25 high genetic differentiation. gt 0.25
very high genetic differentiation.
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FST (FIT - FIS)/(1 - FIS) Where, FIS 1 -
(HI/HS) FST 1 - (HS/HT) FIT 1 - (HI/HT)
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• Scenario 1 -- 5 subpopulations, 1 locus, 2
  alleles
• Given Observed heterozygosity (HI) 0.18
• Pop Xi Xj HIs1-?Xi2
• 1 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 2 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 3 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 4 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 5 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• Ave HS ?HIs/k 0.18
• Ave 0.9 0.1 HT 1 - ?xi2 0.18

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Scenario 1 FIS 1 - (HI/HS) 1 - (0.18/0.18)
0.00 FIT 1 - (HI/HT) 1 - (0.18/0.18)
0.00 FST 1 - (HS/HT) 1 - (0.18/0.18)
0.00 Conclusions No genetic differentiation
among subpopulations No Inbreeding
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• Scenario 2 -- 5 subpopulations, 1 locus, 2
  alleles
• Given Observed heterozygosity (HI) 0.089
• Pop Xi Xj HIs1-?Xi2
• 1 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 2 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 3 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 4 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 5 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• Ave HS ?HIs/k 0.18
• Ave 0.9 0.1 HT 1 - ?xi2 0.18

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Scenario 2 FIS 1 - (HI/HS) 1 - (0.089/0.18)
0.5056 FIT 1 - (HI/HT) 1 - (0.089/0.18)
0.5056 FST 1 - (HS/HT) 1 - (0.18/0.18)
0.00 Conclusions No genetic differentiation
among subpopulations Inbreeding!
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• Scenario 3 -- 5 subpopulations, 1 locus, 2
  alleles
• Given Observed heterozygosity (HI) 0.34
• Pop Xi Xj HIs1-?Xi2
• 1 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 2 0.7 0.3 1-(0.72 0.32) 1 - 0.58 0.42
• 3 0.5 0.5 1-(0.52 0.52) 1 - 0.50 0.50
• 4 0.3 0.7 1-(0.32 0.72) 1 - 0.58 0.42
• 5 0.1 0.9 1-(0.92 0.12) 1 - 0.82 0.18
• Ave HS ?HIs/k 0.34
• Ave 0.5 0.5 HT 1 - ?xi2 0.50

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Scenario 3 FIS 1 - (HI/HS) 1 - (0.34/0.34)
0.00 FIT 1 - (HI/HT) 1 - (0.34/0.50)
0.32 FST 1 - (HS/HT) 1 - (0.34/0.50)
0.32 Conclusions Genetic differentiation
among subpopulations No Inbreeding
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• Scenario 4 -- 5 subpopulations, 1 locus, 2
  alleles
• Given Observed heterozygosity (HI) 0.169
• Pop Xi Xj HIs1-?Xi2
• 1 0.9 0.1 1-(0.92 0.12) 1 - 0.82 0.18
• 2 0.7 0.3 1-(0.72 0.32) 1 - 0.58 0.42
• 3 0.5 0.5 1-(0.52 0.52) 1 - 0.50 0.50
• 4 0.3 0.7 1-(0.32 0.72) 1 - 0.58 0.42
• 5 0.1 0.9 1-(0.12 0.92) 1 - 0.82 0.18
• Ave HS ?HIs/k 0.34
• Ave 0.5 0.5 HT 1 - ?xi2 0.50

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Scenario 4 FIS 1 - (HI/HS) 1 - (0.169/0.34)
0.5029 FIT 1 - (HI/HT) 1 - (0.169/0.50)
0.662 FST 1 - (HS/HT) 1 - (0.34/0.50)
0.32 Conclusions Genetic differentiation
among subpopulations Inbreeding!
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Examples thus far have dealt with a
single hierarchical level. However, there may be
genetic differentiation within subpopulations
which would create additional hierarchical
levels localities within subpopulations. Data
can be partitioned into various
hierarchical levels to determine what
geographical factors most likely explain
population differentiation.
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FST measures the proportion of the total
genetic variation attributable to
subpopulations FST (HT - HS)/ HT
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Conclusions In both scenarios, total genetic
diversity (HT) is 0.4992. However, in scenario
1, 27.3 of the total genetic diversity is
attributable to differences between subpopulations
and only 0.5 is due to differences among
localities within subpopulations.
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Conclusions In scenario 2, 13.4 of the total
genetic diversity is attributable to differences
between the two subpopulation and 1.7 is
attributable to differences among localities.
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Mortamer Snide graduated with a Ph.D. in wildlife
management from Texas AM University in the early
1900s. His dissertation dealt with the
distribution and deer of an unknown and unnamed
mountain range in Idaho. Because of the
rugged terrain and remoteness of the area,
Mortamer spent 15 years collecting observational
data on deer in this area to develop a management
plan. Upon graduating and publishing his
dissertation, Mortamer Snide was hired by the
Idaho Department of Wildlife Resources to
develop a management plan for deer in this area.
Because he spent so much time in these mountains,
the mountain range was officially named the
Mortamer Snide Mountains and the newly developed
management area was named the Mortamer Snide
Management Area. Based on his work, Mortamer
concluded that there were two herds of deer on
the management area, separated from each other by
the Snide Mountain Range. Additionally, his
demographic work suggested that although there
appeared to be subdivision within these two
regions, there were high levels of movement of
individuals within each regions such that each
regions should be treated as a management unit.
Therefore, his management plan was to treat all
deer east of the Snide Mountains as one
management unit and all deer west of the Snide
Mountains as a second management unit. In recent
years, the deer on the Mortamer Snide Management
Area have not been doing well. You are enrolled
in the Ph.D. program at Oklahoma State University
and have become very interested in the problem
with the deer at the Mortamer Snide Management
Area. For your dissertation, you spent several
years performing demographic studies of the deer
on each side of the Snide Mountain Range. Your
observational data indicate that there may
actually be two heards within each region.
However, to test this, you collect blood samples
from several deer from five groups of deer, two
on the west side of the Snide Mountains and three
from the east side of the Snide Mountains and
perform a microsatellite analysis. The following
is a figure illustrating your interpretation of
the demographics of the deer populations on the
Mortamer Snide Management Area. Completely
Analyze these data
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Locus 1 Locus
2 AA Aa aa BB Bb bb A-1 26 27 16 14 19 36 A-
2 10 18 28 38 6 12 B-1 20 23 26 29 14 26 B-2
12 8 36 12 6 38 B-3 19 25 25 30 20 19
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Calculate Observed Heterozygosity (Ho)
Test each locus in each population for deviations
from H.W.E. Sample A1, Locus 1 Ho 27/69
0.3913 A p (262627)/138 0.5725 q 1 -
0.5725 0.4275
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• OBS EXP (O-E)2/E
• 26 (0.5725)2X69 22.62 0.505
• 27 2X0.5725X0.4275X69 33.77 1.357
• 16 (0.4275)2X69 12.61 0.911
• ?2 2.773
• Degrees of Freedom 3 - 1 - 1 1
• Tabled ?2 at ? 0.05 and 1 d.f. 3.84

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• Sample A2, Locus 1
• Ho 18/56 0.321
• A p (101018)/112 0.3393
• q 1 - 0.3393 0.6607
• OBS EXP (O-E)2/E
• 10 (0.3393)2X56 6.47 1.93
• 18 2X0.3393X0.6607X56 25.11 2.01
• 28 (0.6607)2X56 24.45 0.52
• ?2 4.46

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• Sample B1, Locus 1
• Ho 23/69 0.333
• A p (202023)/138 0.4565
• q 1 - 0.4565 0.5435
• OBS EXP (O-E)2/E
• 20 (0.4565)2X69 14.38 2.20
• 23 2X0.4565X0.5435X69 34.24 3.69
• 12 (0.5435)2X69 20.38 3.45
• ?2 9.34

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• Sample B2, Locus 1
• Ho 8/56 0.143
• A p (12128)/112 0.2857
• q 1 - 0.2857 0.7143
• OBS EXP (O-E)2/E
• 12 (0.2857)2X56 4.57 12.08
• 8 2X0.2857X0.7143X56 22.86 9.66
• 36 (0.7143)2X56 28.57 1.93
• ?2 23.67

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• Sample B3, Locus 1
• Ho 25/69 0.362
• A p (191925)/138 0.4565
• q 1 - 0.4565 0.5435
• OBS EXP (O-E)2/E
• 19 (0.4565)2X69 14.38 1.49
• 25 2X0.4565X0.5435X69 34.24 2.49
• 25 (0.5435)2X69 20.38 1.05
• ?2 5.03

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Calculate He 2N(1 - ?pi2)/(2N - 1) A-1 locus
1 1381-(0.32780.1828)/1370.4930 A-1 locus
2 1381-(0.11600.4348)/1370.4525 He (0.4930
0.4525)/2 0.473 A-2 locus 1 1121 -
0.5516/111 0.4524 A-2 locus 2 1121 -
0.6077/111 0.3958 He (0.4524 0.3958)/2
0.4241 B-1 locus 1 1381 - 0.5038/137
0.4998 B-1 locus 2 1381 - 0.5009/137
0.5027 He (0.4998 0.5027)/2 0.5013
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B-2 locus 1 1121 - 0.5918/111 0.4119 B-2
locus 2 1121 - 0.6078/111 0.3856 He
(0.4119 0.3856)/2 0.3988 B-3 locus 1 1381
- 0.5038/137 0.4998 B-3 locus 2 1381 -
0.5114/137 0.4922 He (0.4998 0.4922)/2
0.4960
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FLS FLT FST Locus 1 0.057 0.062 0.004 Locus
2 0.104 0.112 0.008 Ave. 0.081 0.087 0.006
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• F-statistics Locus 1
• HI (0.3910.3210.3330.1430.362)/5 0.399
• Pop Xi Xj HIs1-?Xi2
• A1 0.5725 0.4275 0.4894
• A2 0.3393 0.6607 0.4484
• B1 0.4565 0.5435 0.4962
• B2 0.2857 0.7143 0.4082
• B3 0.4565 0.5435 0.4962
• Ave HS ?HIs/k 0.4677
• Ave 0.4221 0.5779 HT 1 - ?xi2 0.4879

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HI 0.399 HS 0.468 HT 0.488 FIS 1 -
(HI/HS) 1 - (0.399/0.468) 0.147 FIT 1 -
(HI/HT) 1 - (0.399/0.488) 0.182 FST 1 -
(HS/HT) 1 - (0.468/0.488) 0.041
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• F-statistics Locus 2
• HI (0.2750.1070.2030.1070.290)/5 0.196
• Pop Xi Xj HIs1-?Xi2
• A1 0.3406 0.6594 0.4492
• A2 0.7321 0.2679 0.3923
• B1 0.5217 0.4783 0.4991
• B2 0.2678 0.7322 0.3922
• B3 0.5755 0.4245 0.4886
• Ave HS ?HIs/k 0.4443
• Ave 0.4875 0.5125 HT 1 - ?xi2 0.4997

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HI 0.196 HS 0.4443 HT 0.4997 FIS 1 -
(HI/HS) 1 - (0.196/0.444) 0.559 FIT 1 -
(HI/HT) 1 - (0.196/0.500) 0.608 FST 1 -
(HS/HT) 1 - (0.444/0.500) 0.112
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FIS FIT FST Locus 1 0.147 0.182 0.041 Locus
2 0.559 0.608 0.112 Ave 0.353 0.395 0.077
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Calculation of Pairwise FST -- Locus 1
Population A1 vs. A2 Subpop xi xj HSi A1 0.572
5 0.4275 0.4894 A2 0.3393 0.6607 0.4484 HS
0.4689 Ave. 0.4559 0.5441 HT 0.4961 FST 1
- (HS/HT) 1 - (0.4689/0.4961) 0.055
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Locus 2 Population A1 vs. A2 Subpop xi xj HSi
A1 0.3406 0.6594 0.4492 A2 0.7321 0.2679 0.3923
HS 0.4208 Ave. 0.5364 0.4637 HT
0.4975 FST 1 - (HS/HT) 1 - (0.4208/0.4975)
0.154 Ave FST (0.055 0.154)/2 0.105
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Unweighted Pair-Group Method Using
Arithmetric Averages (UPGMA) Clustering
Method. UPGMA computes the average similarity
or dissimilarity of a candidate OTU to an
extant cluster, weighting each OTU in that
cluster equally, regardless of its structural
subdivision.
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Pairwise FST A1 A2 B1 B2 B3 A1 ----- A2 0.105
----- B1 0.024 0.031 ----- B2 0.046 0.110 0.04
8 ----- B3 0.035 0.021 0.001 0.061 --- Step 1
-- Find the pair(s) of OTUs with the lowest value.
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Step 2 -- Recalculate distances with B1,B3 as
an OUT. Differences between OTUs that did not
join any cluster are transcribed unchanged
from the original matrix. Therefore B1,B3 vs.
A1 1/2(B1A1 B3A1) 1/2(0.024 0.035)
0.030 B1,B3 vs. B2 1/2(0.031 0.021)
0.026 B1,B3 vs. B2 1/2(0.048 0.061) 0.055
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Now B1,B3 A1 A2 B2 B1,B3 ----- A1 0.30
----- A2 0.026 0.105 ----- B2 0.055 0.046 0.11
0 ----- Find the smallest difference and repeat
the above steps until all OTUs cluster!
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B1,B3,A2 vs. A1 1/3(0.024 0.035
0.105) 0.055 B1,B3,A2 vs. B2
1/3(0.048 0.061 0.110)
0.073 B1,B2,A2 A1 B2 B1,B2,A2 ----- A
1 0.055 ----- B2 0.073 0.046 -----
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B1,B3,A2 vs. A1,B2 1/6(0.105 0.024
0.035 0.048 0.110 0.061) 0.064 Final
Step is to draw an unrooted dendrogram
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Migration -- movement of individuals (or
their gametes) between populations and
subsequent gene flow. The degree of genetic
differentiation among populations (FST) is
expected to be greater for species with lower
vs. higher dispersal rates subdivided vs.
continuous habitat distant vs. closer
fragments smaller vs. larger population
fragments species with longer vs shorter
divergence times with adaptive differences vs.
those without.
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Change in allele frequency due to migration ?q
m(qm - qt) Frequency of q on the island in the
next generation qt1 qt ?q
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The Mainland-Island model of gene flow
is realistic for the Galapagos Islands west
coast of S. A. habitat islands such as
fragmented rainforests of mountain tops separated
by desert.
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Migration tends to homogenize populations and the
rate of homogenization depends upon the migration
rate, population structure, and difference in
allele frequencies. All subpopulations
eventually approach the mean allele frequency of
the total population! Populations diverge from
each other as a function of genetic drift,
migration, and local selection.
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For example, a pair of populations with a mean
Ne of 1,000 and m 0.01 would not
significantly diverge by chance alone since Nem
10. However, a pair of smaller population, with
a mean Ne of 100 and the same rate of gene
flow (m 0.01), random drift would be greater
and a higher rate of gene flow would be needed to
prevent divergence.
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Some populations and species in nature have
existed for long periods of time in complete
isolation from other gene pools and have diverged
through genetic drift and selection. In such
cases, natural movement among subpopulations was
historically rare or nonexistent and strong
divergence occurred. In such cases, within
population heterozygosity is expected to be low
and FST high, virtually all of the total genetic
diversity (HT) in such species could be due to
the divergence component.
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The management implications of this scenario
is that the separation of these naturally
isolated populations should be maintained. Contra
sting this, is the more typical case in
which genetic exchange among populations occurs
in a hierarchical fashion. In this case, local
populations may be only partially isolated from
other gene pools, with some probability of gene
flow among them.
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Geographically proximate populations would,
on average, experience gene flow more
frequently than would geographically distant
populations. Genetic connectedness is
therefore a function of geographic structure and
spatial scale. Most endangered species do not
experience the equilibrium conditions implicit in
a hierarchical model.
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By their very nature of being endangered or
of special concern, their genetic structure has
probably been altered, populations have been
lost, and remaining populations are dangerously
small and fragmented. Habitat destruction,
blockage of migration routes, drying or diversion
of waterways, clear-cutting, urbanization, and
other anthropogenic factors isolate populations
that normally would experience gene flow with
other populations.
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Genetic divergence among these populations (FST
10.2) was among the highest ever recorded for
birds, much higher than for turkey populations
that had not experienced known bottlenecks. Lebe
rg attributed this divergence to human activity,
including management manipulations.
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Scenarios such as this may call for managers
to simulate natural gene flow by artificial
means. The management challenge in the
hierarchical model is to determine former rates
and direction of gene flow among populations in
an attempt to mimic those rates in the face of
human disturbance.
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The age and sex ratio of translocated
individuals should match the natural history of
the species and care should be taken not to
introduce parasites and pathogens in the
process. This management recommendation is in
direct contrast to the first example -- the
isolated island mode-- in which case the manager
should NOT induce gene flow but rather, should
protect the normal isolation of populations.
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The natural genetic structure of a species and
its normal rates of gene flow may be inferred
from geography historical records knowledge of
the biology of the species genetic information
derived from hierarchical analyses
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Echelle et al. (1987) studied 4 species of
pupfish in the Chihuhan desert region of NM and
TX and their data are amenable to calculating
historical migration rates. Estimated historical
rates of gene flow among populations
Species Distribution FST Nem Cyprinodon
bovines A single, 8km stretch of
spring-fed 1.4 17.6 stream C.
pecosensis 600 - 700 km of mainstream 7.7 3.0
Pecos River C. elegans Spring-fed complex of
canals and 10.8 2.1 creek with partial
isolation C. tularosa 2 isolated springs
associated 19.0 1.1 creek in extremely arid
region
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Nuclear vs. Mitochondrial DNA Nuclear markers
are inherited biparentally and therefore can
provide information concerning both sexes as well
as recombination. Mitochondrial data is only
maternally inherited and therefore only provides
information about matrilines and provides only a
small amount of information.
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• Cronin (1993) proposed that mtDNA data are of
• limited utility because they represent a small
• part of the genome and may not reflect overall
• phylogenetic relationships of taxa.
• Avise provides three arguments for the utility of
• mtDNA in conservation and management.
• In many species, dispersal and gene flow are
• highly asymmetric by gender with females
• often relatively sedentary.

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Gender biased gene flow is exemplified in
many mammalian species by stronger degree of
faithfulness of females to natal sites or
social groups compared with males. In principle,
such behavior should translate into distinctive
population genetic signatures for cytoplasm vs.
nuclear loci.
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Except for those species that release eggs
into the environment, a strong spatial
association normally exists between females and
their newly produced young. If female progeny
remain reasonably philopatric to the natal site
or social group, either by active choice or
passively because of limited dispersal capabilitie
s, a species inevitably will become spatially
structured along matrilines.
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Because recruitment is contingent upon
female reproductive success, any population that
is compromised or extirpated by human or
natural causes, will unlikely recover or
re-establish in the short-term via recruitment of
non-indigenous females when female dispersal is
low.
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From an ecological perspective, each
rookery should be considered (and possibly
managed) as an autonomous demographic
unit. Severe decline or loss of a rookery will
not likely be compensated by natural recruitment
of foreign females.
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