# Assessing beta diversity variations with time

I'm just starting in the field of ecological statistical analysis and I have a few doubts regarding a dataset that I'm working on.
The dataset is composed of several samples collected at a single location during a few months multiple times per day.
From my data I have estimated the beta diversity (Bray-Curtis dissimilarity) and I'd like to know if there is a monotonic trend with time and how much of the diversity can be explained by the different sampling hours or days.
My questions are the following:
- Is the estimation of Mantel's Rho using Spearman correlation is a valid estimator for the linear temporal trend?
- To estimate the source of the diversity (days/hours) would it make sense to run a npmanova analysis (as I'm using R I'd run adonis in particular) using as explanatory variables the sampling hours and dates?

I think the Mantel test is a valid way to test for a correlation, but Spearman is a non-parametric measure of correlation, and will not necessarily test for or estimate a linear trend. A Pearson moment would be better, but you might need to look at your data distributions to see if they fit the assumptions.

In response to the first answer, I don't think Procrustes is the right test for this. It's used for comparing different ordinations, which are dimensionally reduced representations of your dissimilarity matrix data. You lose information when you ordinate a data set, and you want to include as much information as possible when testing hypotheses. Constrained ordination approaches like cannonical correspondance analysis (CCA), or distance-based redundancy analysis (dbRDA) might be more suitable. These are actually analagous to some of the functions performed in adonis.

You should be able to use adonis the way your described. You'll want to make sure you also run betadispersion, which can help assess how suitable your data are. You'll also want to consider how you code your time data. It's simplest if time values are considered as discrete (day 1, day 2, etc.) or categorical (morning, noon, night) variables. Since times of day are cyclical, there's a trick with treating them as a continuous linear variable. Unless you tell it otherwise, a model will treat 23:55 (11:55pm) and 00:05 (12:05am) as being parametrically more distant in time than say 06:00 and 08:00. Depending on your daily sampling window, this might not matter much, but if you want to treat time a continuous, there's a workaround that involves sin() and cos() transformations of the time collections were taken.

It sounds like you're already using Vegan, which is a great package. You might also consider looking into LabDSV, which has a fantastic tutorial page that's more in-depth than most R vignettes. It has good examples of some of the different approaches I mentioned, as well as some others that might be of interest to you.

• Thanks for clarifying my doubts! I used Spearman as a more general approach to see if the correlation was monotonic. I used categorical data for both dates and hours, but I will give the sin/cos transformation a try! Commented May 15, 2020 at 16:11

Rather than Mantel, I would suggest doing a procrustes analysis. I didn't know much about it (and still I don't) but a reviewer required it for a paper I submitted, so I used the implementation in vegan package. You can also give a look at this nice tutorial

The idea of procrustes is similar to Mantel's but it should perform better for this case.

I don't what to say about the second question, sorry!