SimilarityPair: Estimation of two-assemblage similarity measures
In SpadeR: Species-Richness Prediction and Diversity Estimation with R
Description
Usage
Arguments
Value
References
Examples
Description
SimilarityPair: Estimation various similarity indices for two assemblages. The richness-based
indices include the classic two-community Jaccard and Sorensen indices; the abundance-based
indices include the Horn, Morisita-Horn, regional species-overlap, two-community Bray-Curtis and the
abundance-based Jaccard and Sorensen indices. Three types of data are supported: Type (1)
abundance data (datatype="abundance"), Type (2) incidence-frequency data
(datatype="incidence_freq"), and Type (2B) incidence-raw data (datatype="incidence_raw"); see
SpadeR-package details for data input formats.
Usage
1
2
SimilarityPair(X, datatype = c("abundance", "incidence_freq",
"incidence_raw"), units, nboot = 200)
Arguments
X
a matrix/data.frame of species abundances/incidences.
datatype
type of input data, "abundance", "incidence_freq" or "incidence_raw".
units
number of sampling units in each community. For datatype = "incidence_raw", users must specify the number of sampling units taken from each community. This argument is not needed for "abundance" and "incidence_freq" data.
nboot
an integer specifying the number of replications.
Value
a list of ten objects:
$datatype for showing the specified data types (abundance or incidence).
$info for summarizing data information.
$Empirical_richness for showing the observed values of the richness-based similarity indices
include the classic two-community Jaccard and Sorensen indices.
$Empirical_relative for showing the observed values of the equal-weighted similarity indices
for comparing species relative abundances including Horn, Morisita-Horn, regional overlap,
Chao-Jaccard and Chao-Sorensen abundance (or incidence) measures based on species relative abundances.
$Empirical_WtRelative for showing the observed value of the Horn similarity index for comparing
size-weighted species relative abundances based on Shannon entropy under equal-effort sampling.
$Empirical_absolute for showing the observed values of the similarity indices for comparing
absolute abundances. These measures include the Shannon-entropy-based measure,
Morisita-Horn and the regional overlap measures based on species absolute abundances, as well as the Bray-Curtis index.
All measures are valid only under equal-effort sampling.
The corresponding four objects for showing the estimated similarity indices are:
$estimated_richness, $estimated_relative, $estimated_WtRelative and $estimated_Absolute.
References
Chao, A., Chazdon, R. L., Colwell, R. K. and Shen, T.-J. (2005). A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecology Letters, 8, 148-159.
Chao, A., and Chiu, C. H. (2016). Bridging the variance and diversity decomposition approaches to beta diversity via similarity and differentiation measures. Methods in Ecology and Evolution, 7, 919-928.
Chao, A., Jost, L., Hsieh, T. C., Ma, K. H., Sherwin, W. B. and Rollins, L. A. (2015). Expected
Shannon entropy and Shannon differentiation between subpopulations for neutral genes under the finite island model. Plos One, 10:e0125471.
Chiu, C. H., Jost, L. and Chao, A. (2014). Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers. Ecological Monographs, 84, 21-44.
Examples
1
2
3
4
5
6
7
8
9
10
## Not run:
data(SimilarityPairData)
# Type (1) abundance data
SimilarityPair(SimilarityPairData$Abu,"abundance",nboot=200)
# Type (2) incidence-frequency data
SimilarityPair(SimilarityPairData$Inci,"incidence_freq",nboot=200)
# Type (2B) incidence-raw data
SimilarityPair(SimilarityPairData$Inci_raw,"incidence_raw",units=c(19,17),nboot=200)
## End(Not run)
Example output
(1) BASIC DATA INFORMATION:
The loaded set includes abundance/incidence data from 2 communities
and a total of 86 species.
Samples size in Community 1 n1 = 557
Samples size in Community 2 n2 = 111
Number of observed species in Community 1 D1 = 69
Number of observed species in Community 2 D2 = 43
Number of observed shared species in two communities D12 = 26
Number of bootstrap replications for s.e. estimate 200
Some statistics:
f[11]= 4 ; f[1+]= 8 ; f[+1]= 10 ; f[2+]= 2 ; f[+2]= 8 ; f[22]= 0
(2) EMPIRICAL SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity
C02 (q=0, Sorensen) 0.4643 0.0401 0.3857 0.5429
U02 (q=0, Jaccard) 0.3023 0.0303 0.2429 0.3617
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.5502 0.0309 0.4897 0.6108
C22 (q=2, Morisita-Horn) 0.7442 0.0369 0.6719 0.8164
U22 (q=2, Regional overlap) 0.8533 0.0256 0.8032 0.9035
ChaoJaccard-abundance 0.4040 0.0271 0.3509 0.4571
ChaoSorensen-abundance 0.5755 0.0297 0.5173 0.6337
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.6002 0.0286 0.5441 0.6563
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.3894 0.0286 0.3333 0.4455
C22 (Morisita-Horn) 0.3039 0.0389 0.2276 0.3802
U22 (Regional overlap) 0.4661 0.0465 0.3750 0.5573
Bray-Curtis 0.2425 0.0164 0.2103 0.2747
(3) ESTIMATED SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity:
C02 (q=0, Sorensen) 0.4966 0.1579 0.1871 0.8061
U02 (q=0, Jaccard) 0.3303 0.1875 -0.0372 0.6978
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.6763 0.0771 0.5253 0.8274
C22 (q=2, Morisita-Horn) 0.7868 0.0369 0.7144 0.8591
U22 (q=2, Regional overlap) 0.8807 0.0245 0.8327 0.9286
ChaoJaccard-abundance 0.4845 0.0806 0.3265 0.6425
ChaoSorensen-abundance 0.6527 0.0702 0.5151 0.7903
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.7586 0.0715 0.6184 0.8988
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.4922 0.0715 0.3520 0.6324
C22 (q=2, Morisita-Horn) 0.3114 0.0399 0.2332 0.3896
U22 (q=2, Regional overlap) 0.4749 0.0471 0.3825 0.5674
Bray-Curtis 0.2725 0.0410 0.1920 0.3529
NOTE: If an estimate is greater than 1, it is replaced by 1.(1) BASIC DATA INFORMATION:
The loaded set includes abundance/incidence data from 2 communities
and a total of 200 species.
Number of sampling units in Community 1 T1 = 217
Number of sampling units in Community 2 T2 = 62
Number of total incidences in Community 1 U1 = 775
Number of total incidences in Community 2 U2 = 455
Number of observed species in Community 1 D1 = 117
Number of observed species in Community 2 D2 = 103
Number of observed shared species in two communities D12 = 20
Number of bootstrap replications for s.e. estimate 200
Some Statistics:
Q[11]= 2 ; Q[1+]= 6 ; Q[+1]= 7 ; Q[2+]= 2 ; Q[+2]= 3 ; Q[22]= 1
(2) EMPIRICAL SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity
C02 (q=0, Sorensen) 0.1818 0.0249 0.1330 0.2306
U02 (q=0, Jaccard) 0.1000 0.0150 0.0706 0.1294
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.1421 0.0152 0.1124 0.1718
C22 (q=2, Morisita-Horn) 0.0931 0.0194 0.0551 0.1311
U22 (q=2, Regional overlap) 0.1703 0.0107 0.1494 0.1912
ChaoJaccard-abundance 0.1335 0.0163 0.1016 0.1654
ChaoSorensen-abundance 0.2356 0.0259 0.1848 0.2864
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1)
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.1347 0.0162 0.1029 0.1665
C22 (Morisita-Horn) 0.0778 0.0153 0.0478 0.1078
U22 (Regional overlap) 0.1444 0.0265 0.0923 0.1964
Bray-Curtis 0.0813 0.0101 0.0616 0.1010
(3) ESTIMATED SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity:
C02 (q=0, Sorensen) 0.2618 0.0874 0.0905 0.4331
U02 (q=0, Jaccard) 0.1506 0.0669 0.0195 0.2817
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.2286 0.0770 0.0776 0.3796
C22 (q=2, Morisita-Horn) 0.0994 0.2381 0.0000 0.5661
U22 (q=2, Regional overlap) 0.1809 0.0467 0.0894 0.2723
ChaoJaccard-abundance 0.1918 0.0415 0.1105 0.2731
ChaoSorensen-abundance 0.3218 0.0589 0.2064 0.4372
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.2281 0.0791 0.0731 0.3831
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.2168 0.0791 0.0618 0.3719
C22 (q=2, Morisita-Horn) 0.0835 0.0165 0.0512 0.1157
U22 (q=2, Regional overlap) 0.1541 0.0283 0.0987 0.2096
Bray-Curtis 0.1247 0.0346 0.0568 0.1926
NOTE: If an estimate is greater than 1, it is replaced by 1.(1) BASIC DATA INFORMATION:
The loaded set includes abundance/incidence data from 2 communities
and a total of 262 species.
Number of sampling units in Community 1 T1 = 19
Number of sampling units in Community 2 T2 = 17
Number of total incidences in Community 1 U1 = 516
Number of total incidences in Community 2 U2 = 380
Number of observed species in Community 1 D1 = 216
Number of observed species in Community 2 D2 = 130
Number of observed shared species in two communities D12 = 84
Number of bootstrap replications for s.e. estimate 200
Some Statistics:
Q[11]= 16 ; Q[1+]= 28 ; Q[+1]= 33 ; Q[2+]= 15 ; Q[+2]= 18 ; Q[22]= 4
(2) EMPIRICAL SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity
C02 (q=0, Sorensen) 0.4855 0.0240 0.4385 0.5325
U02 (q=0, Jaccard) 0.3206 0.0195 0.2824 0.3588
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.6142 0.0205 0.5741 0.6544
C22 (q=2, Morisita-Horn) 0.6551 0.0177 0.6205 0.6897
U22 (q=2, Regional overlap) 0.7916 0.0105 0.7710 0.8122
ChaoJaccard-abundance 0.5033 0.0234 0.4574 0.5492
ChaoSorensen-abundance 0.6696 0.0229 0.6247 0.7145
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1)
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.6114 0.0204 0.5715 0.6514
C22 (Morisita-Horn) 0.6912 0.0327 0.6270 0.7554
U22 (Regional overlap) 0.8174 0.0249 0.7686 0.8662
Bray-Curtis 0.4821 0.0203 0.4423 0.5220
(3) ESTIMATED SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity:
C02 (q=0, Sorensen) 0.5699 0.0964 0.3810 0.7588
U02 (q=0, Jaccard) 0.3985 0.1004 0.2017 0.5953
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.7368 0.0480 0.6428 0.8308
C22 (q=2, Morisita-Horn) 0.7870 0.0881 0.6143 0.9598
U22 (q=2, Regional overlap) 0.8808 0.0631 0.7570 1.0000
ChaoJaccard-abundance 0.6534 0.0588 0.5382 0.7686
ChaoSorensen-abundance 0.7904 0.0485 0.6953 0.8855
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.7439 0.0461 0.6536 0.8342
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.7315 0.0461 0.6412 0.8218
C22 (q=2, Morisita-Horn) 0.7925 0.0363 0.7214 0.8636
U22 (q=2, Regional overlap) 0.8842 0.0251 0.8350 0.9335
Bray-Curtis 0.5440 0.0277 0.4897 0.5982
NOTE: If an estimate is greater than 1, it is replaced by 1.
SpadeR documentation built on May 2, 2019, 3:59 p.m.
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Description Usage Arguments Value References Examples
Description
SimilarityPair: Estimation various similarity indices for two assemblages. The richness-based
indices include the classic two-community Jaccard and Sorensen indices; the abundance-based
indices include the Horn, Morisita-Horn, regional species-overlap, two-community Bray-Curtis and the
abundance-based Jaccard and Sorensen indices. Three types of data are supported: Type (1)
abundance data (datatype="abundance"), Type (2) incidence-frequency data
(datatype="incidence_freq"), and Type (2B) incidence-raw data (datatype="incidence_raw"); see
SpadeR-package details for data input formats.
Usage
1 2 | SimilarityPair(X, datatype = c("abundance", "incidence_freq",
"incidence_raw"), units, nboot = 200)
|
Arguments
X |
a matrix/data.frame of species abundances/incidences. |
datatype |
type of input data, "abundance", "incidence_freq" or "incidence_raw". |
units |
number of sampling units in each community. For |
nboot |
an integer specifying the number of replications. |
Value
a list of ten objects:
$datatype for showing the specified data types (abundance or incidence).
$info for summarizing data information.
$Empirical_richness for showing the observed values of the richness-based similarity indices
include the classic two-community Jaccard and Sorensen indices.
$Empirical_relative for showing the observed values of the equal-weighted similarity indices
for comparing species relative abundances including Horn, Morisita-Horn, regional overlap,
Chao-Jaccard and Chao-Sorensen abundance (or incidence) measures based on species relative abundances.
$Empirical_WtRelative for showing the observed value of the Horn similarity index for comparing
size-weighted species relative abundances based on Shannon entropy under equal-effort sampling.
$Empirical_absolute for showing the observed values of the similarity indices for comparing
absolute abundances. These measures include the Shannon-entropy-based measure,
Morisita-Horn and the regional overlap measures based on species absolute abundances, as well as the Bray-Curtis index.
All measures are valid only under equal-effort sampling.
The corresponding four objects for showing the estimated similarity indices are:
$estimated_richness, $estimated_relative, $estimated_WtRelative and $estimated_Absolute.
References
Chao, A., Chazdon, R. L., Colwell, R. K. and Shen, T.-J. (2005). A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecology Letters, 8, 148-159.
Chao, A., and Chiu, C. H. (2016). Bridging the variance and diversity decomposition approaches to beta diversity via similarity and differentiation measures. Methods in Ecology and Evolution, 7, 919-928.
Chao, A., Jost, L., Hsieh, T. C., Ma, K. H., Sherwin, W. B. and Rollins, L. A. (2015). Expected
Shannon entropy and Shannon differentiation between subpopulations for neutral genes under the finite island model. Plos One, 10:e0125471.
Chiu, C. H., Jost, L. and Chao, A. (2014). Phylogenetic beta diversity, similarity, and differentiation measures based on Hill numbers. Ecological Monographs, 84, 21-44.
Examples
1 2 3 4 5 6 7 8 9 10 | ## Not run:
data(SimilarityPairData)
# Type (1) abundance data
SimilarityPair(SimilarityPairData$Abu,"abundance",nboot=200)
# Type (2) incidence-frequency data
SimilarityPair(SimilarityPairData$Inci,"incidence_freq",nboot=200)
# Type (2B) incidence-raw data
SimilarityPair(SimilarityPairData$Inci_raw,"incidence_raw",units=c(19,17),nboot=200)
## End(Not run)
|
Example output
(1) BASIC DATA INFORMATION:
The loaded set includes abundance/incidence data from 2 communities
and a total of 86 species.
Samples size in Community 1 n1 = 557
Samples size in Community 2 n2 = 111
Number of observed species in Community 1 D1 = 69
Number of observed species in Community 2 D2 = 43
Number of observed shared species in two communities D12 = 26
Number of bootstrap replications for s.e. estimate 200
Some statistics:
f[11]= 4 ; f[1+]= 8 ; f[+1]= 10 ; f[2+]= 2 ; f[+2]= 8 ; f[22]= 0
(2) EMPIRICAL SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity
C02 (q=0, Sorensen) 0.4643 0.0401 0.3857 0.5429
U02 (q=0, Jaccard) 0.3023 0.0303 0.2429 0.3617
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.5502 0.0309 0.4897 0.6108
C22 (q=2, Morisita-Horn) 0.7442 0.0369 0.6719 0.8164
U22 (q=2, Regional overlap) 0.8533 0.0256 0.8032 0.9035
ChaoJaccard-abundance 0.4040 0.0271 0.3509 0.4571
ChaoSorensen-abundance 0.5755 0.0297 0.5173 0.6337
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.6002 0.0286 0.5441 0.6563
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.3894 0.0286 0.3333 0.4455
C22 (Morisita-Horn) 0.3039 0.0389 0.2276 0.3802
U22 (Regional overlap) 0.4661 0.0465 0.3750 0.5573
Bray-Curtis 0.2425 0.0164 0.2103 0.2747
(3) ESTIMATED SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity:
C02 (q=0, Sorensen) 0.4966 0.1579 0.1871 0.8061
U02 (q=0, Jaccard) 0.3303 0.1875 -0.0372 0.6978
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.6763 0.0771 0.5253 0.8274
C22 (q=2, Morisita-Horn) 0.7868 0.0369 0.7144 0.8591
U22 (q=2, Regional overlap) 0.8807 0.0245 0.8327 0.9286
ChaoJaccard-abundance 0.4845 0.0806 0.3265 0.6425
ChaoSorensen-abundance 0.6527 0.0702 0.5151 0.7903
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.7586 0.0715 0.6184 0.8988
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.4922 0.0715 0.3520 0.6324
C22 (q=2, Morisita-Horn) 0.3114 0.0399 0.2332 0.3896
U22 (q=2, Regional overlap) 0.4749 0.0471 0.3825 0.5674
Bray-Curtis 0.2725 0.0410 0.1920 0.3529
NOTE: If an estimate is greater than 1, it is replaced by 1.(1) BASIC DATA INFORMATION:
The loaded set includes abundance/incidence data from 2 communities
and a total of 200 species.
Number of sampling units in Community 1 T1 = 217
Number of sampling units in Community 2 T2 = 62
Number of total incidences in Community 1 U1 = 775
Number of total incidences in Community 2 U2 = 455
Number of observed species in Community 1 D1 = 117
Number of observed species in Community 2 D2 = 103
Number of observed shared species in two communities D12 = 20
Number of bootstrap replications for s.e. estimate 200
Some Statistics:
Q[11]= 2 ; Q[1+]= 6 ; Q[+1]= 7 ; Q[2+]= 2 ; Q[+2]= 3 ; Q[22]= 1
(2) EMPIRICAL SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity
C02 (q=0, Sorensen) 0.1818 0.0249 0.1330 0.2306
U02 (q=0, Jaccard) 0.1000 0.0150 0.0706 0.1294
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.1421 0.0152 0.1124 0.1718
C22 (q=2, Morisita-Horn) 0.0931 0.0194 0.0551 0.1311
U22 (q=2, Regional overlap) 0.1703 0.0107 0.1494 0.1912
ChaoJaccard-abundance 0.1335 0.0163 0.1016 0.1654
ChaoSorensen-abundance 0.2356 0.0259 0.1848 0.2864
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1)
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.1347 0.0162 0.1029 0.1665
C22 (Morisita-Horn) 0.0778 0.0153 0.0478 0.1078
U22 (Regional overlap) 0.1444 0.0265 0.0923 0.1964
Bray-Curtis 0.0813 0.0101 0.0616 0.1010
(3) ESTIMATED SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity:
C02 (q=0, Sorensen) 0.2618 0.0874 0.0905 0.4331
U02 (q=0, Jaccard) 0.1506 0.0669 0.0195 0.2817
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.2286 0.0770 0.0776 0.3796
C22 (q=2, Morisita-Horn) 0.0994 0.2381 0.0000 0.5661
U22 (q=2, Regional overlap) 0.1809 0.0467 0.0894 0.2723
ChaoJaccard-abundance 0.1918 0.0415 0.1105 0.2731
ChaoSorensen-abundance 0.3218 0.0589 0.2064 0.4372
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.2281 0.0791 0.0731 0.3831
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.2168 0.0791 0.0618 0.3719
C22 (q=2, Morisita-Horn) 0.0835 0.0165 0.0512 0.1157
U22 (q=2, Regional overlap) 0.1541 0.0283 0.0987 0.2096
Bray-Curtis 0.1247 0.0346 0.0568 0.1926
NOTE: If an estimate is greater than 1, it is replaced by 1.(1) BASIC DATA INFORMATION:
The loaded set includes abundance/incidence data from 2 communities
and a total of 262 species.
Number of sampling units in Community 1 T1 = 19
Number of sampling units in Community 2 T2 = 17
Number of total incidences in Community 1 U1 = 516
Number of total incidences in Community 2 U2 = 380
Number of observed species in Community 1 D1 = 216
Number of observed species in Community 2 D2 = 130
Number of observed shared species in two communities D12 = 84
Number of bootstrap replications for s.e. estimate 200
Some Statistics:
Q[11]= 16 ; Q[1+]= 28 ; Q[+1]= 33 ; Q[2+]= 15 ; Q[+2]= 18 ; Q[22]= 4
(2) EMPIRICAL SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity
C02 (q=0, Sorensen) 0.4855 0.0240 0.4385 0.5325
U02 (q=0, Jaccard) 0.3206 0.0195 0.2824 0.3588
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.6142 0.0205 0.5741 0.6544
C22 (q=2, Morisita-Horn) 0.6551 0.0177 0.6205 0.6897
U22 (q=2, Regional overlap) 0.7916 0.0105 0.7710 0.8122
ChaoJaccard-abundance 0.5033 0.0234 0.4574 0.5492
ChaoSorensen-abundance 0.6696 0.0229 0.6247 0.7145
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1)
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.6114 0.0204 0.5715 0.6514
C22 (Morisita-Horn) 0.6912 0.0327 0.6270 0.7554
U22 (Regional overlap) 0.8174 0.0249 0.7686 0.8662
Bray-Curtis 0.4821 0.0203 0.4423 0.5220
(3) ESTIMATED SIMILARITY INDICES:
Estimate s.e. 95%Lower 95%Upper
(a) Classic richness-based similarity:
C02 (q=0, Sorensen) 0.5699 0.0964 0.3810 0.7588
U02 (q=0, Jaccard) 0.3985 0.1004 0.2017 0.5953
(b) Measures for comparing species relative abundances
C12=U12 (q=1, Horn) 0.7368 0.0480 0.6428 0.8308
C22 (q=2, Morisita-Horn) 0.7870 0.0881 0.6143 0.9598
U22 (q=2, Regional overlap) 0.8808 0.0631 0.7570 1.0000
ChaoJaccard-abundance 0.6534 0.0588 0.5382 0.7686
ChaoSorensen-abundance 0.7904 0.0485 0.6953 0.8855
(c) Measures for comparing size-weighted species relative abundances
Horn size-weighted (q=1) 0.7439 0.0461 0.6536 0.8342
(d) Measures for comparing species absolute abundances
C12=U12 (q=1) 0.7315 0.0461 0.6412 0.8218
C22 (q=2, Morisita-Horn) 0.7925 0.0363 0.7214 0.8636
U22 (q=2, Regional overlap) 0.8842 0.0251 0.8350 0.9335
Bray-Curtis 0.5440 0.0277 0.4897 0.5982
NOTE: If an estimate is greater than 1, it is replaced by 1.
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