[R-sig-eco] Vegan metaMDS: unusual first run stress values with large data set

[Ewan Isherwood]

Hello, R-Community! This is the first time writing to this group and
indeed the first time using a mailing list, so please bear with me if
I’ve done something wrong.

I have a large species x site matrix (89 x 4831) that I want to
ordinate using metaMDS in the Vegan (2.0-5) package in R (2.15.2). If
I run this data frame using the Jaccard index in two or more
dimensions (k>1), the first run (run=0) has a relatively low stress
value and the other 20 runs are much higher and have very low
deviation. However, k=1 seems to work fine. Furthermore, a
stress/scree plot reveals a pyramid-like shape, where the k=1 lowest
stress value is low, increases rapidly for k=2 then decreases slowly
as k increases.

Dimensions	Stress
1	0.1382185
2	0.1939509
3	0.1695375
4	0.155221
5	0.1406408
6	0.1294149

I’ve tried this with a small iteration of this data and this issue
arises at k>2 rather than at k>1 as it is here. Anyway, this is the
input and output:

library(vegan)
library(MASS)
PSU <- read.table("PSU.txt", header = TRUE, sep = "")
PSU.sp <- PSU[, 22:110]
PSU.NMDS <- metaMDS(PSU.sp, k=4, zerodist = "add", distance = "jaccard")

Square root transformation
Wisconsin double standardization
Zero dissimilarities changed into  0.0006657301
Run 0 stress 0.155221
Run 1 stress 0.2548103
Run 2 stress 0.255434
Run 3 stress 0.2551382
… (Up to run 20 where run 1 through run 20 have all very similar stress values.)

Call:
metaMDS(comm = PSU.sp, distance = "jaccard", k = 4, zerodist = "add")

global Multidimensional Scaling using monoMDS

Data:     wisconsin(sqrt(PSU.sp))
Distance: jaccard

Dimensions: 4
Stress:     0.155221
Stress type 1, weak ties
No convergent solutions - best solution after 20 tries
Scaling: centring, PC rotation, halfchange scaling
Species: expanded scores based on ‘wisconsin(sqrt(PSU.sp))’

Now, again, with k=1 this does not happen – the solution looks like
any other regular NMDS run. There are no blank values in the data as
they are all numbers between 0 and 100 corresponding to % cover, and
every row and column sum is greater than 0. There are many sites with
the same species configurations, hence the zerodist, but omitting this
makes no difference to the problem at hand. The NMDS works fine if I
use a subset of the data, but I have not subsetted and tested all of
it. Other metric (Euclidean) and nonmetric (Bray) dissimilarity
indices result in the same effect. I’ve chosen k=4 here because of the
(marginal) elbow in the stress plot, but the data itself actually
looks pretty good at any k value. Even though the output is
reasonable, I am concerned that hitting the best solution by a large
amount on the first run means something is messing up, and this
concern is amplified by the strange pyramid shaped stress plot.
Because metaMDS uses random starts, I don't see how this output is
possible. I've scoured the help files and archives of this list and I
am really now at a loss to explain this.

Thank you in advance for your time and consideration!

Ewan