Gas turbine engines, e.g. a turbofan engine, are (is) designed for a specific operating point, for that point the engine operates most efficiently, any deviation from that point causes the air flow in the core of the engine to be of a different volume than the design point flow.
A compressor (or a fan) is designed for a certain compression ratio at a certain rotational speed. When the rotational speed changes (why? reducing the fuel flow causes less hot pressurized gas to be available to expand in the turbine, the less energy is available to compress air), air is compressed less and thus larger in volume. Knowing the passage of the compressor has a fixed cross section per compression stage, less compressed air causes air to flow faster through the stages. As a result the compressor velocity triangles change and blades have a different inflow and as such a different efficiency (lift generation, it can even trigger stall of the blades, unless countermeasures like bleed off-take are taken).
Compressors will work at other conditions than the design condition, the relation is usually displayed in a graph that we call the compressor characteristic (see e.g. What are the "beta lines" of a gas turbine engine component?), this characteristic relates (corrected) flow and pressure ratio to efficiency for given spool speed (using a fictive parameter called the beta lines to ensure a single solution for a given set of parameters is given). The further one moves from the optimum design point, the lower the efficiency (this is not a linear phenomena). Note that gas turbines are aerodynamically balanced and each compressor (or fan) is connected to a turbine (could be through a gearbox) which depends on a similar characteristic. The equilibrium that is reached determines how the engine operating point moves through the compressor characteristic.
When we sweep a fuel flow for a turbofan from high to low at a fixed flight condition (static on the ground), we can plot the results of such an experiment to show the effects of blades receiving the inflow at far less favorable conditions. E.g. the fan operating line:
We can take this further to create an image similar as posted in the question (note that the axes are swapped) for the fan spool speed N1 and the core spool speed N2:
Why the relation is not linear is that the performance depends on various aerodynamic effects (which are not linear) of various components.