  Microbial communities feature an immense diversity of species and this
diversity is linked with outcomes ranging from ecosystem stability to medical
prognoses. Yet the mechanisms underlying microbial diversity are under debate.
While simple resource-competition models don't allow for coexistence of a large
number of species, it was recently shown that metabolic trade-offs can allow
unlimited diversity. Does this diversity persist with more realistic,
intermittent nutrient supply? Here, we demonstrate theoretically that in serial
dilution culture, metabolic trade-offs allow for high diversity. When a small
amount of nutrient is supplied to each batch, the serial dilution dynamics
mimic a chemostat-like steady state. If more nutrient is supplied, diversity
depends on the amount of nutrient supplied due to an "early-bird" effect. The
interplay of this effect with different environmental factors and
diversity-supporting mechanisms leads to a variety of relationships between
nutrient supply and diversity, suggesting that real ecosystems may not obey a
universal nutrient-diversity relationship.
