# #StackBounty: #regression #multivariate-analysis #distance #regression-strategies Determine rate of change in dissimilarity (distance)?

### Bounty: 50

I have repeated measures plant abundance data for 37 forest plots, across 80 years involving 50+ species of plants.

• The data are structured as:
• `Columns` = different species,
• `Rows` = separate samples [Plot-Year combos],
• Each `cell` = abundance (i.e., basal area) of the the given species in the given sample.

Simplified Example (from here):

``````> abund.data

Plot Year Sp1 Sp2 Sp3 Sp4
1   P1    1   1   2   0   0
2   P2    1   1   0   3   2
3   P3    1   0   2   1   0
4   P1    2   1   2   0   0
5   P2    2   1   0   3   2
6   P3    2   0   2   1   0
``````

I’ve calculated a Bray-Curtis dissimilarity (distance) matrix from these data.

``````Continuing the example:
library(ecodist)
distance(abun.data[,-c(1:2)], 'bray')

1         2         3         4         5
2 0.7777778
3 0.3333333 0.7777778
4 0.0000000 0.7777778 0.3333333
5 0.7777778 0.0000000 0.7777778 0.7777778
6 0.3333333 0.7777778 0.0000000 0.3333333 0.7777778
``````

I want to calculate the rate at which plots change in community composition over time.

I had originally run a non-metric multidimensional scaling (NMDS) ordination and wanted to simply calculate changes in NMDS space.

• i.e., I wanted to create change vectors between plot points in subsequent years (I did so here) and then compare the lengths between years using some sort of regression….

`ChangeVectorLength ~ Time | Plot`

However, I don’t think this is valid because of the rank-oriented construction of NMDs ordination.

Is there a way I could do something similar but using the “raw” distance (dissimilarity) values??

• For example (using the example data above): I want to quantify how much the community of species (as a whole) in Plot `P1` has changed from Year `1` to Year `2`.
• However, because the distance matrix represents — well — a matrix of pairwise distances bewteen all points, I’m not sure how to go about quantifying change in “distance space”

Get this bounty!!!

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