How do climate warming affect soil aggregate stability and aggregate-associated phosphorus storage under natural restoration?

•Soil structure became stable after natural restoration.•Warming exerted less effect on the soil structure in restored land.•Warming weaken the protection of P fractions by macroaggregates under natural restoration.•The release risk of available P in smaller-sized aggregates needs to be focused.•Biological factors in P-cycling model help gauge P-fraction climate-change responses.