Whether the same occupancy variables can be added to the first-order and second-order (or higher order) parts of the model

[李治霖]

Hi,

I have two questions about the occuMulti function for Rota multi-species occupancy model in unmarked package.

First, whether the same occupancy variables can be added to the first-order and second-order (or higher order) parts of the model?
For example. there are three species of A, B and C. Both their spatial occupancy (utilization) and interspecific interactions might be potientially affected by elevation. So, can we use the elevation to explain their spatial occupancy and interactions simultaneously. Just like:

stateformulas <- c("~elevation","~elevation","~elevation","~elevation","~elevation","~elevation","elevation")

What I wondered was, if their spatial occupancys were already explained by elevation, could their interspecific relationships not also be explained by elevation?

If that's the case, then:

stateformulas <- c("~elevation","~elevation","~elevation","~1","~1","~1","1")

or

stateformulas <- c("~1","~1","~1","~elevation","~elevation","~elevation","elevation")


Second, how to get the SE and 95%CI when estimating the species interaction factor (SIF) using occuMulti function?

We can get the estimations of  marginal probability of occupancy for species A(ψA) and B(ψB) and the SEs using the code:

ψA <- predict(Multimod, type="state", species="A")
ψB <- predict(Multimod, type="state", species="B")

We can also estimate the occpuancy probability of co-occurrence of A and B(ψAB) and the SE using the code:

ψAB <- predict(Multimod, type="state", species=c('A','B'))

So, using the formula SIF = ψAB/(ψA × ψB) (Mackenzie et al., 2004), we can their SIF estimations, but how to calculate the the SE and 95%CI  for their SIFs?

Any tips would be greatly appreciated! Thanks in advance!

Zhilin Li

[Ken Kellner]

Yes, you can use the same covariates in the first order and higher order terms. Keep in mind it will usually be significantly harder to get good estimates of coefficients for the interaction terms (e.g. requiring many more sites).

There isn't an easy way to get the uncertainty for the SIF. I guess one strategy would be to bootstrap it -

1. Using the estimated coefs and variance-covariance matrix, get a bunch of bootstrap samples of the coefs from a multivariate normal

2. For each bootstrap rep, use the sampled coef vector to calculate the marginal and co-occurrence probabilities (you'd have to do this manually using the math in the Rota paper)

3. Then calculate SIF for each rep yielding a distribution of SIFs, and SEs, etc

More importantly though I'm not sure if the SIF is a useful (or valid) metric for the Rota multispecies model, particularly with >2 species. You already have the estimates of the interaction terms which is a much more direct estimate of the strength of the interaction.

Ken

[李治霖]

Hi Ken,

Thank you for your reply!  It's really difficult to  get the uncertainty for the SIF. But I think, for SIF, the beta values of  interaction terms can reflect the 
overall interaciton of specie pairs. If we want to get the detail interaciton for certain site, SIF is still useful if it is a useful (or valid) metric for the Rota multispecies model.