What TWINSPAN does
TWINSPAN (Two-Way INdicator SPecies ANalysis, Hill 1979) classifies a community data table in the way a vegetation scientist arranges it by hand: it splits the stands into two groups again and again, and it names the species that best indicate each split. Both the stands and the species are classified, hence two-way.
ecan implements it in plain R, so no compiler is needed.
It is not a port of Hill’s original FORTRAN program;
?twinspan lists the known differences.
data(dune, package = "vegan")
tw <- twinspan(dune)
tw
#> TWINSPAN
#> stands: 20
#> pseudospecies: 75
#> cut levels: 0 2 5 10 20
#> divisions: 6
#> groups: 7
#>
#> division 1 at level 0 (n = 20, eig = 0.511)
#> indicators: Ranuflam_1(+) Agrostol_1(+) Eleopalu_1(+) Lolipere_1(-)
#> division 2 at level 1 (n = 13, eig = 0.384)
#> indicators: Hyporadi_1(-)
#> division 3 at level 1 (n = 7, eig = 0.411)
#> indicators: Sagiproc_1(-)
#> division 4 at level 2 (n = 10, eig = 0.317)
#> indicators: Planlanc_1(-)
#> division 5 at level 3 (n = 5, eig = 0.284)
#> indicators: Achimill_1(+)
#> division 6 at level 3 (n = 5, eig = 0.301)
#> indicators: Juncarti_1(+)The steps of one division
Each division is made in three steps.
1. Pseudospecies. TWINSPAN works on presence and
absence, so a quantitative table is first cut into binary pseudospecies
at the cut levels (by default 0, 2, 5, 10, 20). A species
with a cover of 7 is present at the levels 1, 2 and 3, but not at 4 and
5.
psp <- pseudospecies(dune)
dim(psp)
#> [1] 20 75
head(colnames(psp))
#> [1] "Achimill_1" "Agrostol_1" "Airaprae_1" "Alopgeni_1" "Anthodor_1"
#> [6] "Bellpere_1"2. Primary ordination. The first axis of a correspondence analysis of the pseudospecies is found by reciprocal averaging, and the stands are divided at its centroid.
ra <- tw_ra(psp)
ra$eig
#> [1] 0.54038023. Refined and indicator ordination. The division is
then polished using the species that prefer one side of it. The
preference runs from -1 (only in the negative group) to 1 (only in the
positive group), and a pseudospecies is differential when its
absolute preference reaches diff_threshold (1/3 by default,
a frequency ratio of 2:1). Finally a few of the most preferential
pseudospecies are chosen as indicators, which summarise the division
without defining it.
pos <- ra$sample > 0
pref <- tw_preference(psp, pos)
head(sort(pref))
#> Achimill_1 Airaprae_1 Anthodor_1 Bellpere_1 Bromhord_1 Cirsarve_1
#> -1 -1 -1 -1 -1 -1The indicators of every division are shown by print(),
together with the eigenvalue of the axis that made the division (see the
output above).
Classification of the stands
The result gives one row per stand, with the group and the binary path of the divisions that led to it.
head(tw$classification)
#> # A tibble: 6 × 4
#> stand group path depth
#> <chr> <int> <chr> <int>
#> 1 11 1 00 2
#> 2 17 1 00 2
#> 3 19 1 00 2
#> 4 18 2 0100 4
#> 5 5 3 0101 4
#> 6 6 3 0101 4
table(tw$classification$group)
#>
#> 1 2 3 4 5 6 7
#> 3 1 4 4 1 3 4The division tree becomes an hclust object, so the
clustering helpers of ecan and the usual plotting functions
can be used.
Modified TWINSPAN
The original TWINSPAN divides every group of a level before going
deeper, so groups of the same level can differ widely in how
heterogeneous they are. Roleček et al. (2009) instead divide the most
heterogeneous group first, which makes the resulting groups more
comparable. ecan measures the heterogeneity by the total
inertia of the group.
tw_inertia(psp)
#> [1] 2.500848
tw_mod <- twinspan(dune, modified = TRUE, n_clusters = 4)
table(tw_mod$classification$group)
#>
#> 1 2 3 4
#> 3 10 3 4With n_clusters the number of groups is chosen directly,
which the original hierarchy cannot do.
The ordered two-way table
tw_two_way() arranges the stands and the species by
their divisions and shows the cut level of each cell. The digits below
the table are the dichotomy of each stand, and those on the right are
the dichotomy of each species.
tw_two_way(tw)
#> 11115671123498111112
#> 1798 0 234560
#> Cirsarve -----------2-------- 0000
#> Elymrepe ----2---22223------- 0000
#> Bellpere ---22--2-222-------- 0001
#> Bromhord ----2-22-2-2-------- 0001
#> Trifprat ----232------------- 0001
#> Airaprae -22----------------- 00100
#> Empenigr --2----------------- 00100
#> Hyporadi 223----------------- 00100
#> Vicilath 2--1---1------------ 00100
#> Achimill -2--222212---------- 00101
#> Anthodor -22-2222------------ 00101
#> Planlanc 22-23332------------ 00101
#> Lolipere 3--22333333322------ 0011
#> Poaprat 21-22222223222-2---- 0011
#> Rumeacet ----332-----2-2----- 0011
#> Bracruta 2-232322--22222--222 01
#> Poatriv ----323223333223--2- 01
#> Scorautu 32332222-322222222-2 01
#> Trifrepe 2-222323-321222231-- 01
#> Sagiproc 2-2--------32222---- 100
#> Salirepe --22---------------3 100
#> Agrostol ----------2322232233 101
#> Alopgeni ---------2322333--2- 101
#> Juncbufo ------2-----2-22---- 101
#> Ranuflam -------------2-22222 1100
#> Callcusp ----------------2-22 1101
#> Comapalu ----------------22-- 1101
#> Eleopalu -------------2--2332 1101
#> Juncarti ------------22---222 1101
#> Chenalbu ---------------1---- 111
#>
#> 00000000000001111111
#> 00011111111110001111
#> 0000011111
#> 0111100001References
Hill, M.O. (1979) TWINSPAN: a FORTRAN program for arranging multivariate data in an ordered two-way table by classification of the individuals and attributes. Cornell University, Ithaca.
Roleček, J., Tichý, L., Zelený, D. and Chytrý, M. (2009) Modified TWINSPAN classification in which the hierarchy respects cluster heterogeneity. Journal of Vegetation Science 20: 596-602.