Hi Valérie. I am not sure what your distance matrix represents. If it contains dissimilarity in species composition between pairs of communities (sites), with each row or column representing a site, than the matrix resulting from subtraction will contain temporal changes in dissimilarities, but not necessarily changes in species composition. For instance, suppose you have two sites A and B that have completely different species compositions both in the first and in the second year. In this case the subtraction of the distance matrices will indicate no temporal change for this pair of sites. But it does not mean that the species composition within site A has not changed from one year to the other; and the same is valid for site B. I think a better way of estimating temporal changes would be comparing directly the species composition of each site between the two points in time, for instance using a suitable dissimilarity index such as the Bray-Curtis. Then you would have one dissimilarity measure (varying from 0 to 1) for each site, representing how much the species composition has changed from one time to another. If you want a single measure of temporal change for the whole dataset, you can use the average value of the Bray-Curtis index across sites. Anyway, I am curious about the subtraction approach, can you give a reference about it?

Thanks,

Henrique Giacomini

Dear Henrique, thank you very much for your answer. Yes I am working on species communities, with each row representing a site and species are in columns. You are right that changes in dissimilarities may not inform much about changes in composition. However I did not get exactly your suggestion for analysing temporal changes in composition. When analysing changes between for example a treatment with two levels, you have a list of sites, each with an associated factor level. However, if the factor is a temporal variable, you have a paired-design, with each sites sampled twice. I do not know how to compute a distance matrix for such a paired design. Is it allowed to treat the sites as it there were different between the years? For example if you sample 10 sites in two year, you would list them as 20 different sites with the corresponding year as the factor variable?

The reference for the paper:

Baiser et al. (2012) Pattern and process of biotic homogenization in the New Pangaea. Proc. R. Soc. B. doi: 10.1098/rspb.2012.1651

Best,

Valérie

If I correctly understood you have a species x site matrix, and you want to understand which sites present a greater "community variation" in two different periods or years. I think that Mantel test will be a great solution for your problem. Mantel’s test is a correlation between distance matrices (correlogram). Correlograms allow you to compare a species x sites matrix to other matrices that may contain other information like environmental variables or time series. If the dependent matrix is a species similarity and the predictor matrix is a dissimilarity matrix based on a set of environmental variables, then the simple test is for correlation between the two matrices. Such correlation would indicate that locations that are similar environmentally tend to be similar compositionally. If you want to test for time variations on your communities, a first distance matrix is evaluated for all pairs of points within the first distance class; then a second matrix is scored for all pairs of points within the second time interval, and so on.

Moreover Mantel test includes a partial test option: Partial Mantel’s Test on Three Distance Matrices, which is a partial regression on three distance matrices: species dissimilarity, environmental dissimilarity (if sites differ), and in your case time distance. This helps you to understand how much of the variability in species composition is explained by the environmental matrix, and wether residual variability in species composition varies in time after removing the effects of the environmental variables.

On the other hand, perhaps it is useful to measure variables between your sites, to determine if temporal variations in the community composition can be linked to “local” environmental effects. Finally the distance chosen for the analysis is pretty important, are you looking for “overall differences in the community”, the relative changes on functional groups abundances, or rather indicator species. For the first perhaps Bray-Kurtis as Henrique proposed may do it, while an overlap measure (e.g. Morisita-Horn) can do it for the second adding in a second matrix of the mantel some functional characteristics of your species, finally for indicator species chi square distance (CA, CCA) are more likely to help you to find the information you are looking for.

Some references

Raufaste & Rousset (2001). Simple Mantel test when used for the comparison of dendrograms.

P. Legendre and MJ Fortin. 2010. Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data. Molecular Ecology Resources

http://onlinelibrary.wiley.com/doi/10.1111/fwb.12040/pdf

G. S. Cumminget al. 2012. Responses of an African wading bird community to resource pulses are related to foraging guild and food-web position. Freshwater Biology. http://adn.biol.umontreal.ca/~numericalecology/Reprints/Legendre_Fortin_MER_2010.pdf

Hi Valérie, thanks for the paper. What I proposed was to calculate a dissimilarity index for each site, measuring the difference in species composition between the two points in time. If you have quantitative data (species abundances), the Bray-Curtis index is a good one, but if you have presence/absence data, then an index such as the complement of Jaccard's index (i.e. the same they used in the reference you gave me) would be appropriate. In any case, you would arrange species in columns and temporal replicates in rows, and the final result would be a vector of dissimilarities (i.e., if you have 10 sites, then this vector would have 10 elements), instead of a square distance matrix. The problem with this approach is that you would end up with just one (temporal) dissimilarity value for each site, and there would be no simple way of defining the null expectation. The ideal situation would be having replicate samples for the same site in the same time, then it would be possible to test for the significance of the temporal change by comparing the dissimilarities between replicates (of the same site) in different times with dissimilarities between replicates in the same time. But this is not possible if you have only one sample per site per time. The following reference can be useful in this respect:

Phillipi et al. (1998). Detecting trends in species composition. Ecol. App. 8, 300-308.

The alternative would be ignoring that you have a paired design, and analyse differences in composition assuming two independent groups of samples: each group associated with a point in time. Then you would list the sites in a spreadsheet in exactly the same way you proposed above: if you have 10 sites in two years, list then as if they were 20 different sites and add a column identifying time as a factor. In this case, there is a number of analyses that test whether species compositions differ significantly from one time to another. They include ANOSIM and Mantel test. There are also other non-parametric tests, explained in more detail in this reference:

Anderson, M.J. (2001). A new method for non-parametric multivariate analysis

of variance. Austral Ecology 26, 32-46.

The ANOSIM and the Mantel test approaches are detailed in chapter 10 of Legendre & Legendre (1998, 2012) Numerical Ecology.

Softwares that I know to perform these analyses are: Primer (http://www.primer-e.com/) and the Vegan package in R (http://vegan.r-forge.r-project.org/).

best regards

Henrique

Thank you very much for these detailed and very helpful answers! If I correctly get it, what Alex suggests is to have one distance matrix for the first year, one distance matrix for the second year (and possibly one third distance matrix for environmental data)? Then I would compute a Mantel test between the two matrices and it will tell me if sites that are similar in the first year are also similar in the second year. If not significant it will suggest that species communities have changed over time. It is a useful approach, but as Henrique suggested in its first answer, it may not tell a lot about species composition, as two sites may be close in both years despite changes in species composition (well maybe I am looking too far :) ).

I thought about not considering the paired structure as Henrique suggests in the second answer. It would be the more straightforward analysis, but is it allowed? How can we defend this approach for a publication? If sites are closed between years, this should be revealed by the distance matrix. If on the contrary, sites are closer within year, we would get an non-significant result for the factor year as it would be the case for any treatment. Maybe I am wrong.

I just read the method part of "Cumming et al. 2012" indicated by Alex, a study that investigated bird communities over several months in three years. They state in the methods:

"All data were arranged in the same format, with each table having 156 rows that corresponded to each of our 13 sampling sites on each of the 12 missions for which we had matching bird and water quality data".

So it seems that they indeed did not take into account the temporal replicated structure and considered temporal replicated as being independent sites. This possibility may not be ideal, but it is used. Maybe I'll go for it, in combination with mantel test until I find a better way.

The advantage of using a paired design instead of assuming independent samples is that you generally increase the power of the test, because you control for within-subject variability. I suppose it could apply for your data as well. If this is indeed the case, ignoring the paired nature of your data could increase the chance of statistical error type II, i.e. accepting the null hypothesis when it's actually true. Therefore, I would see no problem in your analysis if you carry out a test assuming independent samples and find a significant result. Nevertheless, if the result is not significant, then one could argue that the non-significance was due to low power, and that a more adequate paired test should be used in order to give more conclusive results.

H.

Hi again. Yes Valerie the format of the matrices is as you described. Then I agree with Henrique that the paired design is necessary to consider temporal variations on each site, as if you consider sites on two years as independet samples, you may have uncontroled autocorrelation. That is why you need a test allowing to "eliminate the autocorrelation effect" and assess it's importance. For this mantel test will be pretty helpfull. However it will not provide information of variations between plots in time, but only between plots, and time. So it will not tell you which sites changed more or less between the two years.

On the otherhand can you provide more details about your hypothesis? what your 10 sites represent? are they replicates, or a gradient, series of treatments... do you hypothesize that different sites will respond differently in time?

to explore visually the differences You can carry a suitable ordination method depending on the nature of your data (PCoA or NMDS you can choose a distance of convenience for both), to see how the different communities (sites) change in time.

But if you are interested on internal variations of community structure for each site, then you can use some diversity indexes, like Shannons entropy, or true beta diversity using Hill numbers of Shannon and consider "time turnover of species" for ten units (each of the sites) .

Hi! I sampled insect species in 30 sites, 10 of each of one isolation level. Furthermore they independently varied in the amount of forest in a radius 500m. I replicated my samples in three years. I would like to investigate

1) If there is differences in species community between the three isolation levels

2) If there is differences in species community depending on the amount of forest in the 500m radius

3) If there are differences in species communities between the years (and if possible taking into account the interaction between year and isolation and forest amount)

So quite a lot of questions, but all relate to distance matrices and analyses of species turnover (beta diversity). There are a lot of possible methods (I get a bit lost), some refering directly to species composition, other like Mantel tests rather on correlation between species similarity and environmental similarity...

My main problem is the temporal analysis. I do not know exactly how to take into account the non-independance of the replicated samples.

I get a bit confused between diversity indices and distance matrices. Some papers analyse patterns of beta diversity based on diversity indices and other based on distance matrices. I still did not get exactly the difference, but I think that diversity indices may be more straightforward to look at changes in species composition.

Hi,

If I correctly understood you have you have 10 replicates of 3 degrees of isolation. Isolation can be represented with categorical/hierarchical variable of three levels: 1,2,3. Then you have another variable which is distance of forest, which can be udnerstood as a continuous variable. Time measures are almost for sure autocorrelated, so if you want to use all data you need to eliminate this effect using Mantel test or other similar tool. Then your other two variables can be added as "environmental variables".

However if you are interested in the turnover of species you should take into account that dissimilarity are not really beta, first because they are affected by relative abundance of species, allowing changes even with the same excat composition (with the exception of those based on presence/absence). Moreover, because "dissimilarity indexes" are not metrics they are not performant for multiple comparisons between objects, even if it provides you an idea. True beta diversity should be an independent meausre of species, comparable with alpha and gamma, so must be a single value capable of integrating changes in the populations. For several reasons the only real good beta index is Shannon's entropy. http://www.ecofog.gf/en/perso/Baraloto/publications/Marcon%20et%20al%20Oikos11.pdf and for the calculation of the true beta (independent from alpha) you should use the number of Hill (all described in the paper joint).

I think you may carry different analysis for each of your questions.

First I will try unvariate techniques to ask. Does the number of species, and other diversity indexes changes between plots? and in time? and according to the distance to trees? then test for true beta diversity as well. This can be done with linear or generalized linear models.

Exploratory techniques can be useful, considering that your gradients are short you can use RDA based on euclidean distance (suitable for linear responses). This helps you to ordinate your samples considering differences on sites and adding variables. You can also test CCA which uses chi square distanc, so it tests unimodal distribution of species in your gradient of three levels, if different species responde differently to isolation. Mantel test can help you to correct for autocorrelation.

Finally you can divide your insects in groups e.g. Coleoptera, Hymenoptera, Diptera... as groups or other classification that conveys you and see how they change between your treatments.

Hope these comments were helpful.

Hi Alex, thank you very much! You exactly got the spirit of my study and your answer is really helpful. You mention an important point. The change in beta diversity as a result of relative abundance of species. This is an important issue and I am struggling with it. So you would advise me not to base my study of beta diversity on dissimilarity matrices but rather on Shannon's entropy if I want to take quantitative data into account? Maybe I could combine both: Shannon entropy and dissimilarity matrices for presence-absence data. I will also have a look at db-RDA and CCA.

There are a point that is still not clear to me: how does Mantel test help for removing time effect and other autocorrelation effects? Maybe you can advise me some good literature on this point.

best

Hi, No I don't suggest using one or the other. It depends on what you want to examine. Abundance of species might be an important feature, so using raw counts or trabsformed abundance might be interesting. Ordination using some distances, or dissmilarities can help you to udnerstand which species are important or more abundant on each treatment. But to provide statistical evidence you need to validate with a test. Mantel in this case has been described as a valid method for dealing with autcorrelation on pseudoreplicates:

http://www.bio.umontreal.ca/legendre/reprints/Partial_Mantel_paper.pdf

but also see:

http://arxiv.org/abs/1112.0651

On the other hand if you want to examine general patterns of species successions, then you must use a beta diversity index. All combined as you sais will help you to understand quite well the differences between your plots and the main stressors on species diversity.

Thank you!