Description Usage Arguments Details Value Author(s) References See Also Examples
Function tsallis
find Tsallis diversities with any scale or the corresponding evenness measures. Function tsallisaccum
finds these statistics with accumulating sites.
1 2 3 4 5 |
x |
Community data matrix or plotting object. |
scales |
Scales of Tsallis diversity. |
norm |
Logical, if |
hill |
Calculate Hill numbers. |
permutations |
Usually an integer giving the number
permutations, but can also be a list of control values for the
permutations as returned by the function |
raw |
If |
subset |
logical expression indicating sites (rows) to keep:
missing values are taken as |
theta, phi |
angles defining the viewing
direction. |
col |
Colours used for surface. |
zlim |
Limits of vertical axis. |
... |
Other arguments which are passed to |
The Tsallis diversity (also equivalent to Patil and Taillie diversity) is a one-parametric generalised entropy function, defined as:
H.q = 1/(q-1)(1-sum(p^q))
where q is a scale parameter, S the number of species in
the sample (Tsallis 1988, Tothmeresz 1995). This diversity is concave
for all q>0, but non-additive (Keylock 2005). For q=0 it
gives the number of species minus one, as q tends to 1 this
gives Shannon diversity, for q=2 this gives the Simpson index
(see function diversity
).
If norm = TRUE
, tsallis
gives values normalized by the
maximum:
H.q(max) = (S^(1-q)-1)/(1-q)
where S is the number of species. As q tends to 1, maximum is defined as ln(S).
If hill = TRUE
, tsallis
gives Hill numbers (numbers
equivalents, see Jost 2007):
D.q = (1-(q-1)*H)^(1/(1-q))
Details on plotting methods and accumulating values can be found on
the help pages of the functions renyi
and
renyiaccum
.
Function tsallis
returns a data frame of selected
indices. Function tsallisaccum
with argument raw = FALSE
returns a three-dimensional array, where the first dimension are the
accumulated sites, second dimension are the diversity scales, and
third dimension are the summary statistics mean
, stdev
,
min
, max
, Qnt 0.025
and Qnt 0.975
. With
argument raw = TRUE
the statistics on the third dimension are
replaced with individual permutation results.
Péter Sólymos,
solymos@ualberta.ca, based on the code of Roeland Kindt and
Jari Oksanen written for renyi
Tsallis, C. (1988) Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phis. 52, 479–487.
Tothmeresz, B. (1995) Comparison of different methods for diversity ordering. Journal of Vegetation Science 6, 283–290.
Patil, G. P. and Taillie, C. (1982) Diversity as a concept and its measurement. J. Am. Stat. Ass. 77, 548–567.
Keylock, C. J. (2005) Simpson diversity and the Shannon-Wiener index as special cases of a generalized entropy. Oikos 109, 203–207.
Jost, L (2007) Partitioning diversity into independent alpha and beta components. Ecology 88, 2427–2439.
Plotting methods and accumulation routines are based on
functions renyi
and renyiaccum
. An object
of class 'tsallisaccum' can be used with function
rgl.renyiaccum
as well. See also settings for
persp
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | data(BCI)
i <- sample(nrow(BCI), 12)
x1 <- tsallis(BCI[i,])
x1
diversity(BCI[i,],"simpson") == x1[["2"]]
plot(x1)
x2 <- tsallis(BCI[i,],norm=TRUE)
x2
plot(x2)
mod1 <- tsallisaccum(BCI[i,])
plot(mod1, as.table=TRUE, col = c(1, 2, 2))
persp(mod1)
mod2 <- tsallisaccum(BCI[i,], norm=TRUE)
persp(mod2,theta=100,phi=30)
|
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
32 87 39.46244 19.31897 10.289732 5.982060 3.784873 2.584344 1.882462 1.445176
20 99 44.47873 21.56561 11.366723 6.530095 4.077327 2.746035 1.974163 1.498140
3 89 39.79074 19.34183 10.294475 6.003596 3.814060 2.612130 1.905004 1.461939
8 87 39.98200 19.77567 10.603913 6.181934 3.908381 2.659907 1.928610 1.473408
10 93 41.50369 20.10059 10.639881 6.164157 3.889803 2.648176 1.922207 1.470121
50 92 41.30206 20.08829 10.663128 6.187254 3.906616 2.659292 1.929248 1.474476
23 98 44.40473 21.59625 11.375711 6.520517 4.062575 2.732882 1.964464 1.491646
46 85 38.71044 19.06049 10.224553 5.987209 3.810489 2.611431 1.904913 1.461976
9 89 39.96271 19.39982 10.272025 5.952153 3.761331 2.568371 1.872010 1.438318
5 100 44.20598 21.17686 11.081257 6.350040 3.969940 2.683412 1.937940 1.477217
12 83 37.71285 18.51298 9.908623 5.800306 3.698414 2.543635 1.863626 1.436691
2 83 38.06254 18.90957 10.230614 6.028061 3.848471 2.638667 1.922477 1.472692
1.8 2
32 1.156659 0.9565267
20 1.187661 0.9748589
3 1.168492 0.9646078
8 1.173986 0.9671998
10 1.172341 0.9663808
50 1.174993 0.9679784
23 1.183553 0.9723529
46 1.168556 0.9646728
9 1.152087 0.9534257
5 1.175553 0.9678267
12 1.152998 0.9550599
2 1.174887 0.9683393
32 20 3 8 10 50 23 46 9 5 12 2
TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
0 0.2 0.4 0.6 0.8 1 1.2 1.4
32 1 0.9035303 0.8473994 0.8239937 0.8259777 0.8453403 0.8737041 0.9037309
20 1 0.9168340 0.8714005 0.8563191 0.8638340 0.8853802 0.9124664 0.9383899
3 1 0.8943582 0.8362208 0.8155352 0.8226868 0.8476046 0.8803722 0.9129172
8 1 0.9154260 0.8674322 0.8491531 0.8535754 0.8729254 0.8992501 0.9258854
10 1 0.9001004 0.8450759 0.8255446 0.8324355 0.8561634 0.8872568 0.9180261
50 1 0.9036351 0.8503796 0.8315870 0.8385564 0.8618931 0.8922712 0.9221556
23 1 0.9228895 0.8782744 0.8611017 0.8654544 0.8841064 0.9093061 0.9344888
46 1 0.9032439 0.8485357 0.8278693 0.8331492 0.8554539 0.8856795 0.9162035
9 1 0.8982235 0.8387276 0.8137568 0.8156375 0.8358867 0.8656242 0.8971059
5 1 0.9038026 0.8502581 0.8308757 0.8372445 0.8602030 0.8904867 0.9204832
12 1 0.8971858 0.8367628 0.8114291 0.8136186 0.8347024 0.8655269 0.8980648
2 1 0.9055048 0.8546877 0.8377974 0.8455660 0.8685692 0.8978637 0.9264249
1.6 1.8 2
32 0.9304962 0.9518103 0.9675213
20 0.9594192 0.9746101 0.9847059
3 0.9403687 0.9610574 0.9754460
8 0.9486740 0.9660687 0.9783170
10 0.9438798 0.9632975 0.9767719
50 0.9471031 0.9657020 0.9784999
23 0.9556498 0.9714412 0.9822749
46 0.9422698 0.9621112 0.9760219
9 0.9251745 0.9475646 0.9641383
5 0.9456409 0.9644767 0.9775050
12 0.9269514 0.9498277 0.9665666
2 0.9501791 0.9678597 0.9800060
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