natural selection - Evolution of the haplo-diplontic life cycle

From wikipedia > Biological Life Cycle:

• haplontic life cycle - the haploid stage is multicellular and the diploid stage is a single cell, meiosis is "zygotic".


• diplontic life cycle - the diploid stage is multicellular and haploid gametes are formed, meiosis is "gametic".


• haplodiplontic life cycle [..] - multicellular diploid and haploid stages occur, meiosis is "sporic".

To my knowledge, all mammal species are diplontic. It might even be true for all vertebrates (but I am not sure). In plants and in fungi, there is a much greater diversity of life cycle however. In many (all?) bryophytes for example, the sporophyte (the diploid phase) is multicellular and its life is completely dependent on the gametophyte. This diversity of life cycle lead to the following question:

What drives the evolution of the relative time an organism spend in the haploid vs in the diploid phase of the life cycle?

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_{This post comes as a follow up to @JAD's comment here}