Phosphate fertilization promotes fiber elongation by affecting sucrose inversion, K+ accumulation, and malate synthesis in cotton fiber

•Fiber length increased as the phosphate fertilizer rate increased.•Vmax dominated the increase in fiber length caused by phosphate fertilization.•K+ and malate contributed more to fiber elongation under phosphate fertilization.•Fiber length was relevant to the P content of the leaf subtending the cotton boll.•Two types of P-sensitive cultivars had similar fiber elongation mechanisms.