The statement 'because the microbiome is important for fitness, many organisms have developed specific strategies for passing the microbiome on to progeny' is TRUE. It is natural selection in action.
According to the evolutionary theory proposed by Darwin, natural selection is the mechanism by which species change (evolve) to adapt to particular environmental conditions.
In this case, the microbiome represents an evolutionary adaptive mechanism, thereby natural selection will tend to favor individuals that have a beneficial microbiome.
In consequence, individuals having a beneficial microbiome will have more chances to reproduce and survive (i.e., they have higher adaptive fitness), thereby they also have more chances to pass this adaptive trait to the next generation.
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