I am attempting to model species’ responses to an environmental gradient to characterise their niche in terms of this gradient. I will be using a data on presence/absence of species in grids along this gradient, and a GAM so that I can have flexible shapes and incorporate a number of covariates.

The model will look something like this:

mgcv::gam(occurrence ~ s(gradient, k = 4) + covariates.... family = binomial).

Run for each species separately, with 4 knots to limit things to the anticipated unimodal (or monotonic) shape.

There are standard criteria for deriving parameters to describe species’ niches modelled in this way derived by Heegaard (2002) that I want to use, these are:

Optimum – The value of the gradient where occurrence probability is maximised.

Central Borders – The values of the gradient where occurrence probability is exp(-0.5)*Optimum.

Outer Borders – The values of the gradient where occurrence probability is exp(-2)*Optimum.

Lots of people use these, and I’ve read quite a few papers that do so, but I’m struggling to work out how you’d actually calculate them in practice – it never seems to be described in the papers that I’ve read, and I can’t find code with any of them. I guess this must just be one of those things that is so obvious most people don’t state it, but I’d be grateful if someone could clear it up. This seems like a general question that a lot of people must have when using GAMs.

Is it basically just a case of using predict() to get predicted values of occurrence probability over a very fine grid of the gradient value from the GAM, and extracting the gradient value where occurrence probability is maximised (and so on)? This is the implication of this really helpful answer here, which also has suggestions on how to calculate confidence intervals for these parameters (something I’d also like to do).

Refs

Heegaard, E. (2002). The outer border and central border for species – Environmental relationships estimated by non-parametric generalised additive models. Ecological Modelling, 157(2–3), 131–139. https://doi.org/10.1016/S0304-3800(02)00191-6