Similarity Percentages

Discriminating species between two groups using Bray-Curtis dissimilarities

Usage

simper(comm, group, permutations = 999, parallel = 1, ...)
# S3 method for class 'simper'
summary(object, ordered = TRUE,
    digits = max(3,getOption("digits") - 3), ...)

Arguments

comm: Community data.
group: Factor describing the group structure. If this is missing or has only one level, contributions are estimated for non-grouped data and dissimilarities only show the overall heterogeneity in species abundances.
permutations: a list of control values for the permutations as returned by the function how, or the number of permutations required, or a permutation matrix where each row gives the permuted indices.
object: an object returned by simper.
ordered: Logical; Should the species be ordered by their average contribution?
digits: Number of digits in output.
parallel: Number of parallel processes or a predefined socket cluster. With parallel = 1 uses ordinary, non-parallel processing. (Not yet implemented).
...: Parameters passed to other functions. In simper the extra parameters are passed to shuffleSet if permutations are used.

Details

Similarity percentage, simper (Clarke 1993) is based on the decomposition of Bray-Curtis dissimilarity index (see vegdist, designdist). The contribution of individual species $i$ to the overall Bray-Curtis dissimilarity $d_{jk}$ is given by

$$d_{ijk} = \frac{|x_{ij}-x_{ik}|}{\sum_{i=1}^S (x_{ij}+x_{ik})}$$

where $x$ is the abundance of species $i$ in sampling units $j$ and $k$. The overall index is the sum of the individual contributions over all $S$ species $d_{jk}=\sum_{i=1}^S d_{ijk}$.

The simper functions performs pairwise comparisons of groups of sampling units and finds the contribution of each species to the average between-group Bray-Curtis dissimilarity. Although the method is called “Similarity Percentages”, it really studied dissimilarities instead of similarities (Clarke 1993).

The function displays most important species for each pair of groups. These species contribute at least to 70 % of the differences between groups. The function returns much more extensive results (including all species) which can be accessed directly from the result object (see section Value). Function summary transforms the result to a list of data frames. With argument ordered = TRUE the data frames also include the cumulative contributions and are ordered by species contribution.

The results of simper can be very difficult to interpret and they are often misunderstood even in publications. The method gives the contribution of each species to overall dissimilarities, but these are caused by variation in species abundances, and only partly by differences among groups. Even if you make groups that are copies of each other, the method will single out species with high contribution, but these are not contributions to non-existing between-group differences but to random noise variation in species abundances. The most abundant species usually have highest variances, and they have high contributions even when they do not differ among groups. Permutation tests study the differences among groups, and they can be used to find out the species for which the differences among groups is an important component of their contribution to dissimilarities. Analysis without group argument will find species contributions to the average overall dissimilarity among sampling units. These non-grouped contributions can be compared to grouped contributions to see how much added value the grouping has for each species.

Value

A list of class "simper" with following items:

species: The species names.
average: Species contribution to average between-group dissimilarity.
overall: The average between-group dissimilarity. This is the sum of the item average.
sd: Standard deviation of contribution.
ratio: Average to sd ratio.
ava, avb: Average abundances per group.
ord: An index vector to order vectors by their contribution or order cusum back to the original data order.
cusum: Ordered cumulative contribution. These are based on item average, but they sum up to total 1.
p: Permutation $p$-value. Probability of getting a larger or equal average contribution in random permutation of the group factor. These area only available if permutations were used (default: not calculated).

Author

Eduard Szöcs and Jari Oksanen.

References

Clarke, K.R. 1993. Non-parametric multivariate analyses of changes in community structure. Australian Journal of Ecology, 18, 117–143.

Examples

data(dune)
data(dune.env)
(sim <- with(dune.env, simper(dune, Management, permutations = 99)))
#> cumulative contributions of most influential species:
#> 
#> $SF_BF
#>   Agrostol   Alopgeni   Lolipere   Trifrepe    Poatriv   Scorautu   Bromhord 
#> 0.09824271 0.18254830 0.25956958 0.33367870 0.40734444 0.47729205 0.53120026 
#>   Achimill   Planlanc   Elymrepe   Bracruta 
#> 0.57946526 0.62522255 0.67016196 0.71098133 
#> 
#> $SF_HF
#>   Agrostol   Alopgeni   Lolipere   Planlanc   Rumeacet   Elymrepe    Poatriv 
#> 0.08350879 0.16534834 0.23934930 0.30843624 0.37716139 0.43334492 0.48351753 
#>   Bracruta   Eleopalu    Poaprat   Anthodor   Sagiproc   Trifprat 
#> 0.52804045 0.57205850 0.61423981 0.65549838 0.69628951 0.73696831 
#> 
#> $SF_NM
#>   Poatriv  Alopgeni  Agrostol  Lolipere  Eleopalu   Poaprat  Bracruta  Elymrepe 
#> 0.1013601 0.1935731 0.2667383 0.3377578 0.3999419 0.4526707 0.5044725 0.5505643 
#>  Scorautu  Trifrepe  Sagiproc  Salirepe 
#> 0.5926117 0.6320111 0.6712478 0.7091528 
#> 
#> $BF_HF
#>   Rumeacet    Poatriv   Planlanc   Bromhord   Lolipere   Elymrepe   Trifrepe 
#> 0.08163219 0.15193797 0.21918333 0.27967181 0.33969561 0.39843338 0.45298204 
#>   Anthodor   Achimill   Bracruta   Alopgeni   Trifprat   Juncarti 
#> 0.50276849 0.55222648 0.60021994 0.64584333 0.69126471 0.73366621 
#> 
#> $BF_NM
#>  Lolipere   Poatriv   Poaprat  Trifrepe  Bromhord  Bracruta  Eleopalu  Agrostol 
#> 0.1242718 0.1992126 0.2711756 0.3414609 0.3958520 0.4448077 0.4910724 0.5369083 
#>  Achimill  Scorautu  Anthodor  Planlanc 
#> 0.5823926 0.6253645 0.6638182 0.7012577 
#> 
#> $HF_NM
#>    Poatriv   Lolipere   Rumeacet    Poaprat   Planlanc   Bracruta   Eleopalu 
#> 0.09913221 0.17468460 0.23917190 0.29701331 0.35469313 0.40365488 0.44804851 
#>   Agrostol   Trifrepe   Elymrepe   Anthodor   Juncarti   Trifprat   Salirepe 
#> 0.49226546 0.53434466 0.57564661 0.61543243 0.65341300 0.68921695 0.72432408 
#> 
## IGNORE_RDIFF_BEGIN
summary(sim)
#> 
#> Contrast: SF_BF 
#> 
#>          average      sd   ratio     ava     avb cumsum    p  
#> Agrostol 0.06137 0.03419 1.79490 4.66700 0.00000  0.098 0.05 *
#> Alopgeni 0.05267 0.03648 1.44390 4.33300 0.66700  0.182 0.17  
#> Lolipere 0.04812 0.03945 1.21980 3.00000 6.00000  0.260 0.48  
#> Trifrepe 0.04630 0.02553 1.81380 1.33300 4.66700  0.334 0.06 .
#> Poatriv  0.04602 0.03380 1.36150 4.66700 3.66700  0.407 0.49  
#> Scorautu 0.04370 0.02492 1.75340 1.33300 4.33300  0.477 0.02 *
#> Bromhord 0.03368 0.02586 1.30230 0.50000 2.66700  0.531 0.03 *
#> Achimill 0.03015 0.02082 1.44820 0.16700 2.33300  0.580 0.05 *
#> Planlanc 0.02859 0.02155 1.32650 0.00000 2.00000  0.625 0.58  
#> Elymrepe 0.02807 0.02978 0.94280 2.00000 1.33300  0.670 0.49  
#> Bracruta 0.02550 0.02390 1.06690 2.00000 2.00000  0.711 0.86  
#> Poaprat  0.02513 0.02397 1.04850 2.50000 4.00000  0.751 0.90  
#> Sagiproc 0.02433 0.02215 1.09830 1.83300 0.66700  0.790 0.30  
#> Bellpere 0.01986 0.01709 1.16220 0.66700 1.66700  0.822 0.11  
#> Eleopalu 0.01861 0.04296 0.43330 1.33300 0.00000  0.852 0.87  
#> Anthodor 0.01754 0.02580 0.67980 0.00000 1.33300  0.880 0.81  
#> Juncbufo 0.01603 0.02371 0.67620 1.16700 0.00000  0.905 0.46  
#> Vicilath 0.01467 0.01331 1.10260 0.00000 1.00000  0.929 0.03 *
#> Hyporadi 0.01029 0.01520 0.67680 0.00000 0.66700  0.945 0.63  
#> Ranuflam 0.00931 0.01360 0.68450 0.66700 0.00000  0.960 0.94  
#> Juncarti 0.00698 0.01611 0.43330 0.50000 0.00000  0.972 0.99  
#> Callcusp 0.00698 0.01611 0.43330 0.50000 0.00000  0.983 0.79  
#> Rumeacet 0.00453 0.01044 0.43330 0.33300 0.00000  0.990 0.96  
#> Cirsarve 0.00398 0.00918 0.43360 0.33300 0.00000  0.996 0.34  
#> Chenalbu 0.00233 0.00537 0.43330 0.16700 0.00000  1.000 0.36  
#> Airaprae 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Comapalu 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Empenigr 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Salirepe 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Trifprat 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Contrast: SF_HF 
#> 
#>          average      sd   ratio     ava     avb cumsum    p   
#> Agrostol 0.04738 0.03127 1.51510 4.66700 1.40000  0.084 0.29   
#> Alopgeni 0.04643 0.03290 1.41150 4.33300 1.60000  0.165 0.19   
#> Lolipere 0.04199 0.02701 1.55460 3.00000 4.00000  0.239 0.76   
#> Planlanc 0.03920 0.03321 1.18040 0.00000 3.00000  0.308 0.02 * 
#> Rumeacet 0.03899 0.02737 1.42470 0.33300 3.20000  0.377 0.01 **
#> Elymrepe 0.03188 0.02955 1.07870 2.00000 2.00000  0.433 0.43   
#> Poatriv  0.02847 0.02152 1.32270 4.66700 4.80000  0.484 1.00   
#> Bracruta 0.02526 0.02104 1.20040 2.00000 2.80000  0.528 0.93   
#> Eleopalu 0.02497 0.03888 0.64240 1.33300 0.80000  0.572 0.80   
#> Poaprat  0.02393 0.01918 1.24780 2.50000 3.40000  0.614 0.98   
#> Anthodor 0.02341 0.02143 1.09230 0.00000 1.80000  0.655 0.61   
#> Sagiproc 0.02314 0.02048 1.13010 1.83300 0.80000  0.696 0.41   
#> Trifprat 0.02308 0.02343 0.98500 0.00000 1.80000  0.737 0.01 **
#> Juncarti 0.02285 0.02568 0.88990 0.50000 1.60000  0.777 0.45   
#> Trifrepe 0.02238 0.01949 1.14860 1.33300 2.80000  0.817 0.94   
#> Juncbufo 0.02164 0.02224 0.97330 1.16700 1.20000  0.855 0.23   
#> Scorautu 0.02051 0.01642 1.24890 1.33300 2.80000  0.891 0.79   
#> Achimill 0.01518 0.01139 1.33260 0.16700 1.20000  0.918 0.73   
#> Bromhord 0.01338 0.01450 0.92220 0.50000 0.80000  0.941 0.81   
#> Ranuflam 0.01066 0.01339 0.79640 0.66700 0.40000  0.960 0.93   
#> Bellpere 0.00999 0.01257 0.79480 0.66700 0.40000  0.978 0.92   
#> Callcusp 0.00662 0.01508 0.43930 0.50000 0.00000  0.989 0.97   
#> Cirsarve 0.00381 0.00867 0.43940 0.33300 0.00000  0.996 0.57   
#> Chenalbu 0.00221 0.00503 0.43930 0.16700 0.00000  1.000 0.50   
#> Airaprae 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Comapalu 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Empenigr 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Hyporadi 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Salirepe 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Vicilath 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Contrast: SF_NM 
#> 
#>          average      sd   ratio     ava     avb cumsum    p   
#> Poatriv  0.07828 0.04095 1.91180 4.66700 0.00000  0.101 0.01 **
#> Alopgeni 0.07122 0.04696 1.51670 4.33300 0.00000  0.194 0.01 **
#> Agrostol 0.05651 0.04418 1.27920 4.66700 2.16700  0.267 0.03 * 
#> Lolipere 0.05485 0.05991 0.91550 3.00000 0.33300  0.338 0.14   
#> Eleopalu 0.04803 0.04717 1.01820 1.33300 2.16700  0.400 0.04 * 
#> Poaprat  0.04072 0.03179 1.28100 2.50000 0.66700  0.453 0.02 * 
#> Bracruta 0.04001 0.03440 1.16310 2.00000 2.83300  0.504 0.14   
#> Elymrepe 0.03560 0.03852 0.92430 2.00000 0.00000  0.551 0.10 . 
#> Scorautu 0.03247 0.03481 0.93280 1.33300 3.16700  0.593 0.11   
#> Trifrepe 0.03043 0.03163 0.96190 1.33300 1.83300  0.632 0.66   
#> Sagiproc 0.03030 0.03048 0.99430 1.83300 0.50000  0.671 0.03 * 
#> Salirepe 0.02928 0.03201 0.91440 0.00000 1.83300  0.709 0.03 * 
#> Anthodor 0.02454 0.03669 0.66880 0.00000 1.33300  0.741 0.56   
#> Callcusp 0.02276 0.02944 0.77310 0.50000 1.16700  0.770 0.06 . 
#> Ranuflam 0.02257 0.02282 0.98890 0.66700 1.33300  0.800 0.08 . 
#> Juncarti 0.02254 0.02860 0.78830 0.50000 1.16700  0.829 0.46   
#> Hyporadi 0.02011 0.03129 0.64260 0.00000 1.16700  0.855 0.19   
#> Juncbufo 0.01986 0.02903 0.68400 1.16700 0.00000  0.881 0.32   
#> Planlanc 0.01542 0.02277 0.67720 0.00000 0.83300  0.900 0.97   
#> Airaprae 0.01488 0.02188 0.68020 0.00000 0.83300  0.920 0.06 . 
#> Bellpere 0.01232 0.01592 0.77370 0.66700 0.33300  0.936 0.67   
#> Comapalu 0.01188 0.01741 0.68260 0.00000 0.66700  0.951 0.09 . 
#> Achimill 0.00929 0.01493 0.62240 0.16700 0.33300  0.963 1.00   
#> Bromhord 0.00717 0.01633 0.43910 0.50000 0.00000  0.972 0.96   
#> Rumeacet 0.00559 0.01275 0.43840 0.33300 0.00000  0.980 0.98   
#> Empenigr 0.00523 0.01200 0.43540 0.00000 0.33300  0.986 0.30   
#> Cirsarve 0.00478 0.01089 0.43910 0.33300 0.00000  0.993 0.01 **
#> Chenalbu 0.00289 0.00660 0.43820 0.16700 0.00000  0.996 0.02 * 
#> Vicilath 0.00279 0.00642 0.43450 0.00000 0.16700  1.000 0.82   
#> Trifprat 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Contrast: BF_HF 
#> 
#>          average      sd   ratio     ava     avb cumsum    p  
#> Rumeacet 0.03867 0.02606 1.48380 0.00000 3.20000  0.082 0.06 .
#> Poatriv  0.03330 0.02579 1.29110 3.66700 4.80000  0.152 0.87  
#> Planlanc 0.03185 0.01830 1.74010 2.00000 3.00000  0.219 0.36  
#> Bromhord 0.02865 0.01799 1.59260 2.66700 0.80000  0.280 0.06 .
#> Lolipere 0.02843 0.02215 1.28340 6.00000 4.00000  0.340 0.95  
#> Elymrepe 0.02782 0.02959 0.94040 1.33300 2.00000  0.398 0.50  
#> Trifrepe 0.02584 0.01656 1.56030 4.66700 2.80000  0.453 0.74  
#> Anthodor 0.02358 0.02042 1.15470 1.33300 1.80000  0.503 0.63  
#> Achimill 0.02343 0.01474 1.58930 2.33300 1.20000  0.552 0.18  
#> Bracruta 0.02273 0.01802 1.26170 2.00000 2.80000  0.600 0.87  
#> Alopgeni 0.02161 0.02308 0.93630 0.66700 1.60000  0.646 0.89  
#> Trifprat 0.02151 0.02207 0.97470 0.00000 1.80000  0.691 0.18  
#> Juncarti 0.02008 0.02555 0.78600 0.00000 1.60000  0.734 0.67  
#> Scorautu 0.01932 0.01357 1.42410 4.33300 2.80000  0.774 0.77  
#> Bellpere 0.01829 0.01486 1.23050 1.66700 0.40000  0.813 0.13  
#> Agrostol 0.01761 0.02284 0.77080 0.00000 1.40000  0.850 1.00  
#> Juncbufo 0.01500 0.02066 0.72600 0.00000 1.20000  0.882 0.61  
#> Vicilath 0.01285 0.01140 1.12740 1.00000 0.00000  0.909 0.02 *
#> Sagiproc 0.01168 0.01297 0.90080 0.66700 0.80000  0.934 0.88  
#> Eleopalu 0.01017 0.02111 0.48170 0.00000 0.80000  0.955 0.93  
#> Hyporadi 0.00895 0.01312 0.68240 0.66700 0.00000  0.974 0.68  
#> Poaprat  0.00720 0.01010 0.71330 4.00000 3.40000  0.989 1.00  
#> Ranuflam 0.00508 0.01055 0.48170 0.00000 0.40000  1.000 0.96  
#> Airaprae 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Chenalbu 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Cirsarve 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Comapalu 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Empenigr 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Salirepe 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> Callcusp 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA  
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Contrast: BF_NM 
#> 
#>          average      sd   ratio     ava     avb cumsum    p   
#> Lolipere 0.09068 0.02644 3.42900 6.00000 0.33300  0.124 0.01 **
#> Poatriv  0.05468 0.04465 1.22500 3.66700 0.00000  0.199 0.33   
#> Poaprat  0.05251 0.01813 2.89700 4.00000 0.66700  0.271 0.02 * 
#> Trifrepe 0.05129 0.02756 1.86100 4.66700 1.83300  0.342 0.02 * 
#> Bromhord 0.03969 0.02920 1.35900 2.66700 0.00000  0.396 0.01 **
#> Bracruta 0.03572 0.02869 1.24500 2.00000 2.83300  0.445 0.43   
#> Eleopalu 0.03376 0.03573 0.94500 0.00000 2.16700  0.491 0.46   
#> Agrostol 0.03345 0.03473 0.96300 0.00000 2.16700  0.537 0.85   
#> Achimill 0.03319 0.02338 1.42000 2.33300 0.33300  0.582 0.01 **
#> Scorautu 0.03136 0.02026 1.54800 4.33300 3.16700  0.625 0.26   
#> Anthodor 0.02806 0.03295 0.85200 1.33300 1.33300  0.664 0.37   
#> Planlanc 0.02732 0.02193 1.24600 2.00000 0.83300  0.701 0.50   
#> Salirepe 0.02677 0.02927 0.91400 0.00000 1.83300  0.738 0.11   
#> Bellpere 0.02353 0.01909 1.23200 1.66700 0.33300  0.770 0.02 * 
#> Hyporadi 0.02172 0.02450 0.88600 0.66700 1.16700  0.800 0.26   
#> Ranuflam 0.02031 0.02275 0.89300 0.00000 1.33300  0.828 0.26   
#> Elymrepe 0.01999 0.02926 0.68300 1.33300 0.00000  0.855 0.86   
#> Callcusp 0.01783 0.02681 0.66500 0.00000 1.16700  0.880 0.50   
#> Juncarti 0.01769 0.02600 0.68100 0.00000 1.16700  0.904 0.66   
#> Vicilath 0.01577 0.01447 1.09000 1.00000 0.16700  0.925 0.02 * 
#> Sagiproc 0.01543 0.01857 0.83100 0.66700 0.50000  0.947 0.81   
#> Airaprae 0.01341 0.01969 0.68100 0.00000 0.83300  0.965 0.32   
#> Comapalu 0.01074 0.01571 0.68400 0.00000 0.66700  0.980 0.35   
#> Alopgeni 0.01000 0.01463 0.68300 0.66700 0.00000  0.993 0.99   
#> Empenigr 0.00479 0.01105 0.43300 0.00000 0.33300  1.000 0.44   
#> Chenalbu 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Cirsarve 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Juncbufo 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Rumeacet 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Trifprat 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Contrast: HF_NM 
#> 
#>          average      sd   ratio     ava     avb cumsum    p   
#> Poatriv  0.07155 0.01368 5.23000 4.80000 0.00000  0.099 0.01 **
#> Lolipere 0.05453 0.02962 1.84100 4.00000 0.33300  0.175 0.23   
#> Rumeacet 0.04655 0.03081 1.51100 3.20000 0.00000  0.239 0.01 **
#> Poaprat  0.04175 0.01885 2.21500 3.40000 0.66700  0.297 0.04 * 
#> Planlanc 0.04163 0.02956 1.40800 3.00000 0.83300  0.355 0.01 **
#> Bracruta 0.03534 0.02010 1.75800 2.80000 2.83300  0.404 0.38   
#> Eleopalu 0.03204 0.03231 0.99200 0.80000 2.16700  0.448 0.56   
#> Agrostol 0.03192 0.02889 1.10500 1.40000 2.16700  0.492 0.93   
#> Trifrepe 0.03037 0.02287 1.32800 2.80000 1.83300  0.534 0.65   
#> Elymrepe 0.02981 0.03868 0.77100 2.00000 0.00000  0.576 0.56   
#> Anthodor 0.02872 0.02480 1.15800 1.80000 1.33300  0.615 0.27   
#> Juncarti 0.02741 0.02854 0.96100 1.60000 1.16700  0.653 0.18   
#> Trifprat 0.02584 0.02597 0.99500 1.80000 0.00000  0.689 0.01 **
#> Salirepe 0.02534 0.02729 0.92900 0.00000 1.83300  0.724 0.14   
#> Alopgeni 0.02446 0.03240 0.75500 1.60000 0.00000  0.758 0.92   
#> Scorautu 0.02070 0.01412 1.46600 2.80000 3.16700  0.787 0.85   
#> Ranuflam 0.01928 0.01994 0.96700 0.40000 1.33300  0.814 0.37   
#> Juncbufo 0.01818 0.02465 0.73800 1.20000 0.00000  0.839 0.46   
#> Hyporadi 0.01714 0.02655 0.64600 0.00000 1.16700  0.863 0.36   
#> Callcusp 0.01683 0.02490 0.67600 0.00000 1.16700  0.886 0.42   
#> Achimill 0.01656 0.01490 1.11100 1.20000 0.33300  0.909 0.70   
#> Sagiproc 0.01528 0.01653 0.92400 0.80000 0.50000  0.930 0.84   
#> Airaprae 0.01261 0.01824 0.69100 0.00000 0.83300  0.947 0.25   
#> Bromhord 0.01209 0.01517 0.79700 0.80000 0.00000  0.964 0.85   
#> Comapalu 0.01011 0.01456 0.69400 0.00000 0.66700  0.978 0.27   
#> Bellpere 0.00880 0.01373 0.64100 0.40000 0.33300  0.990 0.95   
#> Empenigr 0.00454 0.01033 0.43900 0.00000 0.33300  0.997 0.55   
#> Vicilath 0.00240 0.00546 0.43900 0.00000 0.16700  1.000 0.88   
#> Chenalbu 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> Cirsarve 0.00000 0.00000     NaN 0.00000 0.00000  1.000   NA   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> Permutation: free
#> Number of permutations: 99
## IGNORE_RDIFF_END