In a plant’s life cycle, how many sporophyte generations occur between one gametophyte generation and the next time that eggs and sperm are produced?

Ans.

Plants that show distinct asexual diploid and sexual haploid stages show alternation of generations. In these plants, the sexual haploid stage (or multi-cellular gametophyte generation), with n number of chromosomes alternates with asexual diploid stage (multi-cellular sporophyte generation), with 2n chromosomes.  

The gametophyte produces gametes (eggs and sperms) that forms zygote and develop into microsporophyte that develops into sporophytes. After maturation, sporophytes produces spores that form gametophytes and again formation of gametes (eggs and sperms) will take place.

Hence, 'one sporophyte generation would occur between the one gametophyte generation and production of eggs and sperms in next steps.'

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when it is at an intermediate population density