Be careful in your starting assumption that current environmental or habitat variables have anything at all to do with coexistence.  The two species could simply partition the resource by for example feeding at different times of the day on exactly the same resource, or by feeding higher on a tree than each other.  Modeling a suite of physical or biotic variables may be fun, but it may have virtually nothing to do with determining coexistence.  Yes, you may discover correlations, but they may not resolve themselves as causal factors.  Also, it is important to remember that historical evolution of the two species is an important factor determining the range of each, independent of comtemporary ecology,  A single event in the history of the species may explain its presence in the range of another.  This is nicely revealed by the accidental or purposeful release of an exotic invasive or the re-release of a previously extirpated species back into its historic range.  The new species moves in and spreads (e.g., coyote).  It may or may not displace a simllar species(e.g., fox).  But for a long period of time both will coexist - having little or nothing to do with how each has mutually accommodated to factors you have anthropogenically decided to measure and put into a model.

Dear Miguel,

The SIMPER (Similarity Percentage) is a simple method for assessing which variables are primarily responsible for an observed difference between groups of samples. The overall significance of the difference is often assessed by ANOSIM. The Bray-Curtis similarity measure (multiplied with 100) is most commonly used with SIMPER, but the Euclidean, cosine and chord measures can also be used.

I wish you good luck with your analysis.

Thanks Tanim! As far as I know SIMPER is best suited for analysis of community data and here I am working only with 2 species. 

Best, MIguel.

r-value can be a proxy

Thanks Abhijit,

that was my first idea, to run model selection for each species and compare which variables are selected in each model.

Thanks Rodrigo!

That sounds promising!

Hi Miguel! Nice to hear from you again :) My first answer would have been ANOSIM too.  I've asked to a friend that maybe had  a similar dataset (I'll tell you something as soon as possible). Good luck and a big hug!

Thanks Laura! ;)

Cayetano just gave me some good references to look at:

Latent Variable Models (Letten et al 2015).

cooccur() library in R (Veech 2013, 2014)

Big hug to you too!

Dear Miguel

You may try these methodologies

Mantel Test (e.g. Velásquez, Johanna, and Juan A. Sánchez. “Octocoral Species Assembly and Coexistence in Caribbean Coral Reefs.” Ed. Chaolun Allen Chen. PLoS ONE 10.7 (2015): e0129609. PMC. Web. 24 Aug. 2015.)

Environment-based methods (e.g. Pausas JG, Verdú M. The Jungle of Methods for Evaluating Phenotypic and Phylogenetic Structure of Communities. BioScience [Internet]. Oxford University Press (OUP); 2010 Sep;60(8):614–25. Available from: http://dx.doi.org/10.1525/bio.2010.60.8.7).

I hope this may help you

Regards

Jose Macedo

Thanks Jose!

That sounds interesting! I am leaving you all here a couple of interesting references that I got from my colleague Cayetano Guitierrez Cánovas:

http://onlinelibrary.wiley.com/doi/10.1111/1365-2745.12428/abstract

https://cran.r-project.org/web/packages/cooccur/cooccur.pdf

Dear Miguel,

it sounds like "metaMDS" from the "vegan" package in R could be your weapon of choice for a robust visual assessment (and subsequent analysis using the ordination scores). Have a look at this vignette: http://cc.oulu.fi/~jarioksa/opetus/metodi/vegantutor.pdf . Under 3. you can find methods of plotting environmental data to your ordination.

I used the vegan nmds ordination to compare microhabitat choices of 8 species, and was able to generate very clean, intuitive plots that are telling most of the (complex) story, and eventually made it into the manuscript for publication.

Moritz

Thanks Mortiz!

I'll have a look at it.

Dear Migueal,

Maybe try SEM - structural equetion modeling

An advantage is a use of apriori knowledge about the relations, possibility to include unknown relations (i think it works via latent variables) and a possibility to include both direct and indirect relations. My guess is that works actually better with the one or two species occurrence / performance than e.g. a community response. Also if you have a linear relations (or you expect such) it would work better (although other types can also be  included).

best regards

Agata

Thanks Miguel

Those references are quite important in understanding plant coexistence

Be careful in your starting assumption that current environmental or habitat variables have anything at all to do with coexistence.  The two species could simply partition the resource by for example feeding at different times of the day on exactly the same resource, or by feeding higher on a tree than each other.  Modeling a suite of physical or biotic variables may be fun, but it may have virtually nothing to do with determining coexistence.  Yes, you may discover correlations, but they may not resolve themselves as causal factors.  Also, it is important to remember that historical evolution of the two species is an important factor determining the range of each, independent of comtemporary ecology,  A single event in the history of the species may explain its presence in the range of another.  This is nicely revealed by the accidental or purposeful release of an exotic invasive or the re-release of a previously extirpated species back into its historic range.  The new species moves in and spreads (e.g., coyote).  It may or may not displace a simllar species(e.g., fox).  But for a long period of time both will coexist - having little or nothing to do with how each has mutually accommodated to factors you have anthropogenically decided to measure and put into a model.

Occupancy Rates

http://warnercnr.colostate.edu/~gwhite/mark/markhelp/occupancy_estimation_royle_nichols.htm

Hola Miguel,

With just two species, even though you measured multiple factors, multivariate ordination might not be necessary… I assume that from your matrix it is possible to build “profiles” for these two species and then simply comparing these profiles will show their similarities and differences… also Kolmogorov-Smirnov test seems to be usable for testing whether these “profiles” differ from each other significantly or not.

Suerte

Hi Zaal,

you are right, with just 2 species there is no need for multivariate ordination. Building some kind of niche profiles and comparing them might be the way to go.

Thanks!

Dear Miguel,

If you wish to use any equations for the analysis, Lotka-Volterra model developed for "predator-prey" situation is appeared to be the best. This model is suitable in the case of competition for food resources as well. For the analysis without equations the singular spectrum analysis is suitable.

Thanks Alexey!

I will consider competition models too.

Best, Miguel.