How do both autotrophic and heterotrophic successions end up having Gross Production = Respiration?
The author is saying that 1) Mature ecosystems tend to have a balance between production (=P) and use (=R, respiration) of biomass. This is actually tautological because the author would probably define a mature ecosystem as one where this is true (P=R).

If it starts out P > R, the autotrophs are dominant: more biomass is being produced than used up. It is possible, for a time, that P will increase as, for example, plants grow more leaves, but R is growing too, and there is an eventual limit on P, which at maximum depends on the light available to the ecosystem. As biomass grows, so does the amount of biomass to potentially decay, so eventually R will always catch up to P, until there is balance.

If it starts out P &lt; R, that means you are using up biomass faster than you are creating it. This case is even simpler: you will gradually run out of biomass, and R will decrease.

In either case, when the author is talking about P = R, this is going to be in relative terms; there might still be variations between them, for example seasonal variation, but on average over years or decades you would expect P = R in a mature, stable ecosystem.