How do GDM knots relate to spline coefficients?

Hello,

I want to identify the sub-intervals of environmental gradients with the greatest species turnover rate from a fitted GDM (gdm::gdm) by calculating rise over run for each spline/segment.

I fitted models with 5 splines (default is 3) and allowed automatic definition of knots (via quantiles). The sum of spline coefficients for each predictor equals the height of the overall function on the y-axis.

However, GDM outputs include 5 knots and 5 spline coefficients per fitted predictor, with the lowest and highest values of the knots representing the extremes of the gradients in the predictor data. I had assumed each coefficient refers to the additional y-axis height attained in each segment/sub-interval along the gradients as defined by knots, but 5 knots only gives four segments (i.e. knot1 ? function1 ? knot2 ? function2 ? knot3 ? function3 ? knot4 ? function4 ? knot5).

Can anyone explain how individual splines are related to the knots (i.e. Given same number of knots as coefficients) so that I can work out which gradient sub-interval goes with each coefficient?

Cheers,
Greg Guerin