Sampling
for
Variety
Matti Miestamo
Dik Bakker
Antti Arppe
Overview
Sampling for Variety
2
Overview
1. Introduction: Probability vs Variety Sampling
Sampling for Variety
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Overview
1. Introduction: Probability vs Variety Sampling
2. Looking for Variety
Sampling for Variety
4
Overview
1. Introduction: Probability vs Variety Sampling
2. Looking for Variety
3. The Experiment: DV versus GM
Sampling for Variety
5
Overview
1. Introduction: Probability vs Variety Sampling
2. Looking for Variety
3. The Experiment: DV versus GM
4. Conclusions
Sampling for Variety
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1. Probability vs Variety Sampling
Sampling for Variety
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Linguistic data analysis
Analysis
Sampling for Variety
Report
8
Linguistic data analysis
Analysis
Report
All languages of the world: only guarantee that no existing possibility is
missed (cf extinct & future languages )
Sampling for Variety
9
Linguistic data analysis
Analysis
Report
All languages of the world:
- Impossible: gaps in description, time considerations etc.
Sampling for Variety
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Linguistic data analysis
Analysis
Report
All languages of the world
- Impossible
Sampling for Variety
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Tendencies & Correlations
Analysis
All languages of the world
- Impossible
- Not desired
Sampling for Variety
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Tendencies & Correlations
Analysis
Tendencies
&
Correlations
All languages of the world
- Impossible
- Not desired
Sampling for Variety
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Tendencies & Correlations
Analysis
Tendencies
&
Correlations
All languages of the world
- Impossible
- Not desired
Sampling for Variety
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Exploring Existing Variety
Analysis
All languages of the world
- Impossible
- Not desired
- Not necessary
Sampling for Variety
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Exploring Existing Variety
Analysis
Existing
Variety
All languages of the world
- Impossible
- Not desired
- Not necessary
Sampling for Variety
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Exploring Existing Variety
Analysis
Existing
Variety
All languages of the world
- Impossible
- Not desired
- Not necessary
Sampling for Variety
17
Exploring Existing Variety
Analysis
Sampling for Variety
Existing
Variety
18
2. Looking for Variety
Sampling for Variety
19
Variety Sampling
Some methods that could be applied for finding variety:
Sampling for Variety
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Variety Sampling
Some methods that could be applied for finding variety:
1. Tomlin (1986)
Sampling for Variety
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Variety Sampling
Some methods that could be applied for finding variety:
1. Tomlin (1986)
2. Dryer (1989)
Sampling for Variety
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Variety Sampling
Some methods that could be applied for finding variety:
1. Tomlin (1986)
2. Dryer (1989)
3. Nichols (1992)
Sampling for Variety
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Variety Sampling
Some methods that could be applied for finding variety:
1. Tomlin (1986)
2. Dryer (1989)
3. Nichols (1992)
4. Bybee, Perkins & Pagliuca (1994)
Sampling for Variety
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Variety Sampling
Some methods that could be applied for finding variety:
1. Tomlin (1986)
2. Dryer (1989)
3. Nichols (1992)
4. Bybee, Perkins & Pagliuca (1994)
…
Sampling for Variety
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Variety Sampling
Some methods designed for finding variety:
Sampling for Variety
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Variety Sampling
Some methods designed for finding variety:
A. Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
Sampling for Variety
27
Variety Sampling
Some methods designed for finding variety:
A. Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
- All independent families represented, extra number of languages
taken from each grouping determined by their Diversity Value
Sampling for Variety
28
Variety Sampling
Some methods designed for finding variety:
A. Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
- All independent families represented, extra number of languages
taken from each grouping determined by their Diversity Value
- No areal stratification
Sampling for Variety
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Variety Sampling
Some methods designed for finding variety:
A. Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
- All independent families represented, number of languages
taken from each grouping determined by their Diversity Value
- No areal stratification
- Problem: dependent on the details of classifications, but these
are often uncertain and incommensurable across the world
Sampling for Variety
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Variety Sampling
Some methods designed for finding variety:
A. Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
- All independent families represented, exrtra number of languages
taken from each grouping determined by their Diversity Value
- No areal stratification
- Problem: dependent on the details of classifications, but these
are often uncertain and incommensurable across the world
B. Miestamo (2003, 2005) – GM method
Sampling for Variety
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Variety Sampling
Some methods designed for finding variety:
A. Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
- All independent families represented, number of languages
taken from each grouping determined by their Diversity Value
- No areal stratification
- Problem: dependent on the details of classifications, but these
are often uncertain and incommensurable across the world
B. Miestamo (2003, 2005) – GM method
- All Genera (Dryer 1989) are represented
Sampling for Variety
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Variety Sampling
Some methods designed for finding variety:
A. Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
- All independent families represented, number of languages
taken from each grouping determined by their Diversity Value
- No areal stratification
- Problem: dependent on the details of classifications, but these
are often uncertain and incommensurable across the world
B. Miestamo (2003, 2005) – GM method
- All Genera (Dryer 1989) are represented
- Areal stratification > Macro-areas (Dryer 1989)
Sampling for Variety
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Variety Sampling
Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
Miestamo (2003, 2005) – GM method
Comparison DV versus GM method:
Sampling for Variety
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Variety Sampling
Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
Miestamo (2003, 2005) – GM method
Comparison DV versus GM method:
- specifically designed for variety sampling
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Variety Sampling
Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
Miestamo (2003, 2005) – GM method
Comparison DV versus GM method:
- specifically designed for variety sampling
- most explicit general methods available
Sampling for Variety
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Variety Sampling
Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
Miestamo (2003, 2005) – GM method
Comparison DV versus GM method:
- specifically designed for variety sampling
- most explicit general methods available
- implemented computationally
Sampling for Variety
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Variety Sampling
Rijkhoff & al. (1993); Rijkhoff & Bakker (1998) – DV method
Miestamo (2003, 2005) – GM method
Comparison DV versus GM method:
- specifically designed for variety sampling
- most explicit general methods available
- implemented computationally
- replicable
Sampling for Variety
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A. Diversity Value method
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Diversity Value method
Basis: Tree-shaped Genealogical classification (e.g. Ethnologue-16
Ethnologue-15
WALS
Ruhlen 1991
Voegelin&Voegelin
…)
Sampling for Variety
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Diversity Value method
Basis: Tree-shaped Genealogical classification
Basic Sample (BS): one language per family (= highest node)
Sampling for Variety
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Diversity Value method
Basis: Tree-shaped Genealogical classification
Basic Sample (BS): one language per family (= highest node)
Ethn-15
147
WALS
209
Ruhlen
22
minimum sample size
Sampling for Variety
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Diversity Value method
Basis: Tree-shaped Genealogical classification
Basic Sample (BS): one language per family (= highest node)
Small Sample (< minimum)
Sampling for Variety
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Diversity Value method
Basis: Tree-shaped Genealogical classification
Basic Sample (BS): one language per family (= highest node)
Small Sample (< minimum):
Random (1 per family)
Sampling for Variety
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Diversity Value method
Basis: Tree-shaped Genealogical classification
Basic Sample (BS): one language per family (= highest node)
Small Sample (< minimum):
Random (1 per family)
Extended Sample (> minimum)
Sampling for Variety
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Diversity Value method
Basis: Tree-shaped Genealogical classification
Basic Sample (BS): one language per family (= highest node)
Small Sample (< minimum):
Random (1 per family)
Extended Sample (> minimum):
1 + DV value
Sampling for Variety
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Diversity Value method
Extended Sample:
1 + DV value
DV value: weight of a family tree based on recursively
calculated complexity of all subtrees
Sampling for Variety
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
Sampling for Variety
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
Fam_k
Sampling for Variety
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
>
Sampling for Variety
Fam_k
50
Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=3
>
Sampling for Variety
Fam_k
DV=2
51
Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=3
=
Sampling for Variety
Fam_k
DV=3
52
Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=3
Fam_k
DV=3
9
Sampling for Variety
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=3
Fam_k
DV=3
6
9
Sampling for Variety
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=7.5
Fam_k
DV=3
4.5
6
9
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=7.5
Fam_k
DV=6
4.5
3.0
6
9
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=7.5
>
Fam_k
DV=6
4.5
3.0
6
9
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Diversity Value method
Extended Sample:
1 + DV value
DV value:
Fam_i
DV=7.5
Fam_k
DV=6
etcetera …
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Diversity Value method
Extended Sample:
1 + DV value
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Diversity Value method
Extended Sample:
1 + DV value
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Diversity Value method
Extended Sample:
1 + DV value
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Diversity Value method
Extended Sample:
1 + DV value
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B. Genus Macro-area method
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Genus Macro-area method
Basis: Genealogical  Genera (Dryer 1989, 2005, 2008)
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Genus Macro-area method
Basis: Genealogical  Genera (Dryer 1989, 2005, 2008)
- Time depth comparable
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Genus Macro-area method
Basis: Genealogical  Genera (Dryer 1989, 2005, 2008)
- Time depth comparable
- Widely accepted
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Genus Macro-area method
Basis: Genealogical  Genera (Dryer 1989, 2005, 2008)
- Time depth comparable
- Relatively uncontroversial
- Relatively large size
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
How to establish a GM sample of a specific size?
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n
< 475
Sampling for Variety
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n < 475
Sampling for Variety
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n < 475
Sampling for Variety
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n < 475
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n < 475 ( RANDOM MOD FAMILY )
Africa:
7 Families:
70 > 15
deleted
iteratively
from largest
family
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n < 475
Sampling for Variety
75
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n < 475
Sampling for Variety
76
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n < 475
Sampling for Variety
77
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n
> 475
Sampling for Variety
78
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n > 475
Sampling for Variety
79
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n > 475 ( RANDOM MOD FAMILY )
Sampling for Variety
80
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n > 475 ( RANDOM MOD FAMILY )
Iteratively
assigned to
proportionally
least
represented
family
wrt genera
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Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n > 475
Sampling for Variety
82
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n > 475
Sampling for Variety
83
Genus Macro-area method
Genus Sample (GS):
1 language per Genus (n=475)
Basic Sample (BS):
n > 475
…
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Variety Sampling
Variety Sampling:
which method is the best?
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3. The Experiment: DV versus GM
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DV versus GM
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DV versus GM
Procedure:
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DV versus GM
Procedure:
1. Generate a sample of size S1, S2, S3, … for both DV and GM
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DV versus GM
Procedure:
1. Generate a sample of size S1, S2, S3, … for both DV and GM
2. Compare variety for each sample Sn for DV and GM
Sampling for Variety
90
DV versus GM
Procedure:
1. Generate a sample of size S1, S2, S3, … for both DV and GM
2. Compare variety for each sample Sn for DV and GM
3. Determine which of the two has highest average variety
Sampling for Variety
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DV versus GM
Procedure:
1. Generate a sample of size S1, S2, S3, … for both DV and GM
2. Compare variety for each sample Sn for DV and GM
3. Determine which of the two has highest average variety
Points:
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DV versus GM
Procedure:
1. Generate a sample of size S1, S2, S3, … for both DV and GM
2. Compare variety for each sample Sn for DV and GM
3. Determine which of the two has highest average variety
Points:
a. Which classification(s) to use?
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93
DV versus GM
Procedure:
1. Generate a sample of size S1, S2, S3, … for both DV and GM
2. Compare variety for each sample Sn for DV and GM
3. Determine which of the two has highest average variety
Points:
a. Which classification(s)?
b. Which typological variables to measure variety on?
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94
DV versus GM
Procedure:
1. Generate a sample of size S1, S2, S3, … for both DV and GM
2. Compare variety for each sample Sn for DV and GM
3. Determine which of the two has highest average variety
Points:
a. Which classification(s)?
b. Which typological variables?
c. How test?
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DV versus GM
a. Which classification(s)?
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DV versus GM
a. Which classification(s)?
DV: must have ‘depth’:
Ethnologue (#15); n of lgs = 7299
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DV versus GM
a. Which classification(s)?
DV: must have ‘depth’:
Ethnologue (#15); n of lgs = 7299
GM: must have genera:WALS; n of lgs = 2561
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DV versus GM
b. Which typological variables?
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99
DV versus GM
b. Which typological variables?
WALS database:
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100
DV versus GM
b. Which typological variables?
WALS database:
- 138 variables (phon/morph/synt/lex/…): representative
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DV versus GM
b. Which typological variables?
WALS database:
- 138 variables (phon/morph/synt/lex/…)
- 2 – 9 different values
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DV versus GM
b. Which typological variables?
WALS database:
- 138 variables (phon/morph/synt/lex/…)
- 2 – 9 different values
- value distribution frequent < - > rare
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DV versus GM
b. Which typological variables?
WALS database:
- 138 variables (phon/morph/synt/lex/…)
- 2 – 9 different values
- value distribution frequent < - > rare
- total 2511 languages with 1 or more values
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DV versus GM
b. Which typological variables?
WALS database:
- 138 variables (phon/morph/synt/lex/…)
- 2 – 9 different values
- value distribution frequent < - > rare
- total 2511 languages with 1 or more values
- value for 415 languages on average per variable
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DV versus GM
c. How test?
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DV versus GM
c. How test?
1. For each variable Vi (i = 1 - 138) in the WALS database:
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DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of 18 sample sizes Sn (n=50, 100, 150, …, 900):
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DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
3. For each method M (DV, GM):
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DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
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DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
5. This gives n nodes (family, group, genus) in C
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DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
5. This gives n nodes (family, group, genus) in C
6. Randomly select a language for each node from C
Sampling for Variety
112
DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
5. This gives n nodes (family, group, genus) in C
6. Randomly select a language for each node from C
7. For each language determine value (1-9) for Vi in WALS, or 0
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DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
5. This gives n nodes (family, group, genus) in C
6. Randomly select a language for each node from C
7. For each language determine value for Vi in WALS, or 0
8. Add value to value set Vi.Sn
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114
DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
5. This gives n nodes (family, group, genus) in C
6. Randomly select a language for each node from C
7. For each language determine value for Vi in WALS, or 0
8. Add value to value set Vi.Sn
9. Compare completeness Vi.Sn for DV and GM
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115
DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
138 x
18 x
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
5. This gives n nodes (family, group, genus) in C
6. Randomly select a language for each node from C
7. For each language determine value for Vi in WALS, or 0
8. Add value to value set Vi.Sn
9. Compare completeness Vi.Sn for DV and GM
100 x
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DV versus GM
c. How test?
1. For each variable Vi in the WALS database:
2. For a series of sample sizes Sn:
18 x
138 x
3. For each method M (DV, GM):
4. Generate sample Vi.Sn on the basis of M-specific classification C
5. This gives n nodes (family, group, genus) in C
6. Randomly select a language for each node from C
7. For each language determine value for Vi in WALS, or 0
8. Add value to value set Vi.Sn
9. Compare completeness Vi.Sn for DV and GM
100 x
= 250,200 samples per method
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DV versus GM
Key factors (0.0 = LOW, 1.0 = HIGH)
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118
DV versus GM
Key factors
Saturation (SAT):
proportion of values for variable in a sample
0.0: no values found
1.0: all values (2-9) found
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119
DV versus GM
Key factors
Saturation (SAT):
proportion of values for variable in a sample (0.0 – 1.0)
Completeness (COMP):
number of draws necessary to find all values
0.0: maximum (=100 draws) reached
1.0: all values found in first draw
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DV versus GM
Key factors
Saturation (SAT):
proportion of values for variable in a sample (0.0 – 1.0)
Completeness (COMP):
number of draws necessary to find all values (0.0 – 1.0)
Several more, not discussed here …
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121
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
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122
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
Sampling for Variety
123
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
Sampling for Variety
124
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
GM > DV
GM > DV
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125
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
5028
languages
with no
value!!!
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126
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
Sampling for Variety
Only
languages
with a
value!!!
127
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
Sampling for Variety
128
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
Sampling for Variety
129
DV versus GM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
DV > GM
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130
DV versus GM
DV slightly better overall than GM, but:
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DV versus GM
DV slightly better overall than GM, but:
A. Differences per sample size?
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132
DV versus GM
DV slightly better overall than GM, but:
A. Differences per sample size?
B. Differences per feature?
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133
DV versus GM
A. Sample size:
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134
DV versus GM
A. Sample size:
1. SATuration
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135
DV versus GM
A. Sample size:
1. SATuration
Sampling for Variety
136
DV versus GM
A. Sample size:
1. SATuration
DV ≈ GM
DV > GM
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137
DV versus GM
A. Sample size:
2. COMPleteness
Sampling for Variety
138
DV versus GM
A. Sample size:
GM > DV
2. COMPleteness
DV > GM
Sampling for Variety
139
DV versus GM
A. Sample size:
GM improves around sample size 450 - 500
Sampling for Variety
140
DV versus GM
A. Sample size:
GM improves around sample size 450 - 500
GM: number of genera = 475
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141
DV versus GM
A. Sample size:
GM improves around sample size 450 - 500
GM: number of genera = 475
> support for genera?
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142
DV versus GM
B. Feature:
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DV versus GM
B. Feature:
Sampling for Variety
144
DV versus GM
Factor?
B. Feature:
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DV versus GM
How GOOD are DV and GM?
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DV versus GM
How GOOD are DV and GM?
Compare with RANDOM sample of same size:
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DV vs GM vs RANDOM
MEAN over FEATURES (138) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
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DV vs GM vs RANDOM
MEAN over FEATURES (138) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
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DV vs GM vs RANDOM
DV & GM > RAN
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150
DV vs GM vs RANDOM
MEAN over FEATURES (139) * SAMPLE SIZES (50, 100, … , 900)
N of draws per Feature * SampleSize: 100
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DV vs GM vs RANDOM
DV & GM > RAN
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4. Conclusions
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Conclusions
1. As an explorative device, Variety Sampling works
better at any common sample size (50-900) than
Random Sampling:
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Conclusions
1. As an explorative device, Variety Sampling works
better at any common sample size (50-900) than
Random Sampling:
a. to find maximum variety
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Conclusions
1. As an explorative device, Variety Sampling works
better at any common sample size (50-900) than
Random Sampling:
a. to find maximum variety
b. to establish it relatively easily
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Conclusions
1. As an explorative device, Variety Sampling works
better at any common sample size (50-900) than
Random Sampling:
a. to find maximum variety
b. to establish it relatively easily
(c. all other measures …)
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Conclusions
2. A purely genealogically based method (DV) works
slightly better for smaller samples (< 500) than a
method which combines a genealogical basis with
areal stratification (GM).
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Conclusions
2. A purely genealogically based method (DV) works
slightly better for smaller samples (< 500) than a
method which combines a genealogical basis with
areal stratification (GM).
For larger samples both methods are equally good,
but areal stratification may make it easier to find
the optimal sample.
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Conclusions
3. Unclear why areal stratification does not simply
improve genealogical sampling
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Conclusions
3. Unclear why areal stratification does not simply
improve genealogical sampling
- Macro-Areas too crude  AutoTyp areas?
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Conclusions
3. Unclear why areal stratification does not simply
improve genealogical sampling
- Macro-Areas too crude  AutoTyp areas?
- Areal under/overrepresentation of Genera
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Conclusions
3. Unclear why areal stratification does not simply
improve genealogical sampling
- Macro-Areas too crude  AutoTyp areas?
- Areal under/overrepresentation of Genera
- Try other diversity criteria (e.g. Dahl 2008)
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Conclusions
3. Unclear why areal stratification does not simply
improve genealogical sampling
- Macro-Areas too crude  AutoTyp areas?
- Areal under/overrepresentation of Genera
- Try other diversity criteria (e.g. Dahl 2008)
GOAL: find optimal balance Areal vs Genealogical
stratification
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?
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