I am a novice in Generalized Additive Models (GAMs) and I would need some advice on these models. From capture data, I would like to assess the effect of longitudinal changes in proportion of forests on abundance of skunks. To test this, I built this GAM where the dependent variable is the number of unique skunks and the independent variables are the X coordinates of the centroids of trapping sites (called "X" in the GAM) and the proportion of forests within the trapping sites (called "prop_forest" in the GAM):

Code:

```
mod <- gam(nb_unique ~ s(x,prop_forest), offset=log_trap_eff, family=nb(theta=NULL, link="log"), data=succ_capt_skunk, method = "REML", select = TRUE)
summary(mod)
Family: Negative Binomial(13.446)
Link function: log
Formula:
nb_unique ~ s(x, prop_forest)
Parametric coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.02095 0.03896 -51.87 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Approximate significance of smooth terms:
edf Ref.df Chi.sq p-value
s(x,prop_forest) 3.182 29 17.76 0.000102 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
R-sq.(adj) = 0.37 Deviance explained = 49%
-REML = 268.61 Scale est. = 1 n = 58
```

Is it correct to include the interaction between X and proportion of forests when my objective is to test longitudinal changes in proportion of forests?

Thanks a lot for your time.

Have a nice day.

Marine