Pairwise spatial co-occurrence

[Luke Emerson]

Hi Jeff and Everyone, 

I am in need of some advice on the best modelling approach to use to determine species pairwise spatial co-occurrence from camera trap surveys for a carnivore guild of 13 species.

I have been working through the online vignettes for the spOccupancy package, they are SOOOOOO helpful, thank you for this amazing resource and package!!

I have 2 independent study areas that are different forest types (so these will be analysed separately). Each study area contains 50 or more camera stations. Surveys were conducted across several years (up to 10 years) at these camera stations for each study area. Each camera station ran for several weeks during each survey period. Each study area contains approximately 13 carnivore species for which I want to determine pairwise spatial co-occurrence / overlap scores on a scale of 0 to 1. 

I want a spatial co-occurrence score between 0 and 1 because I am assessing potential competition between each species pair within the carnivore guild across multiple niche axes including temporal activity, body mass, and diet. My analysis framework currently calculates an overlap score between 0 and 1 for each niche axis (0 = no overlap and 1 = complete overlap). I then take the mean of these overlap scores to calculate a total overlap / potential for competition for each species pair within the guild, hence I need the spatial co-occurrence / overlap value to be on scale of 0 to 1.

Would you recommend using spatial multi-species occupancy models and then calculating the occupancy probability at each station for each species, then determining the probability of occupancy for both species at each station, then averaging across all stations and surveys to determine mean co-occurrence probability for study area?

I.e. 

1. Calculate Occupancy Probabilities (ψ) for Each Species at each camera station

2. Calculate Co-occurrence Probability for species 1 (ψ1​) and species 2 (ψ2​) at each camera station: P(co-occurrence) = ψ1 ​× ψ2​

3. Average Co-occurrence Probability for the species pair across all stations: Average Co-occurrence = 1/N ​ N∑i=1 ​(ψ1,i ​× ψ2,i​),  where N is the total number of stations.

 OR

Would you recommend just running individual two-species single season occupancy models for each species pair, perform any required model selection process, and simply take the co-occurrence values from the best performing model for each species pair? (I wasn't planning on running multi-season models because I am not really concerned if occupancy is changing over time).

OR perhaps you would recommend something else ... ?

Any advice is much appreciated.

Kind regards,

Luke Emerson

[Jeffrey Doser]

Hi Luke,

Glad to hear you have found the online resources helpful! I think the two approaches you have outlined there both seem reasonable, but given the number of species you have, I would probably suggest going with the spatial multi-species model route, since you would need to fit a substantial number of two-species models using the second approach. You could also do a deeper dive into some of the other types of multi-species model (e.g., the occuMulti function in unmarked) that could also be useful for your situation, but I think working with 12 species might be a bit much for those types of models (although I could certainly be wrong). The approach you outline with the spatial multi-species model would certainly do the trick, and since everything is Bayesian in spOccupancy you should be able to derive full posterior distributions for all of your derived calculations, which would allow you to have credible intervals and uncertainty estimates for all your derived parameters.

As a bit of an aside, I might also suggest explicitly fitting a multi-season model, particularly given your interest in quantifying co-occurrence. If you assume occupancy probability is constant across the entire period, I think it may decrease the ecological interpretation of any co-occurrence values you calculate, since the species could "occupy" the same site but actually never occur there together (e.g., if one species used the site for the first 5 years and then another used it for the second 10 years). So, it might be worthwhile exploring a spatial multi-species multi-season model (stMsPGOcc in spOccupancy), and in your calculations of average co-occurrence probability you would just have another summation over the different "seasons" as well.

Anyways, hope that helps!

Jeff

[Luke Emerson]

Hi Jeff,

Thanks for the useful advice, that's great. I really appreciate it!

Regards,

Luke :)