Abstract
Microbial collectives can perform functions beyond the capability of individual members. Enhancing collective functions through artificial selection is, however, challenging. Here, we explore the 'rafting-a-waterfall' metaphor where achieving a target population composition depends on both target and initial compositions. Specifically, collectives comprising fast-growing (F) and slow-growing (S) individuals were grown for 'maturation' time, and the collective with S-frequency closest to the target value is chosen to 'reproduce' via inoculating offspring collectives. During collective maturation, intra-collective selection acts like a waterfall, relentlessly driving the S-frequency to lower values, while during collective reproduction, inter-collective selection resembles a rafter striving to reach the target frequency. Using simulations and analytical calculations, we show that intermediate target S frequencies are the most challenging, akin to a target within the vertical drop of a waterfall, rather than above or below it. This arises because intra-collective selection is the strongest at intermediate S-frequencies, which can overpower inter-collective selection. While achieving a low target S frequencies is consistently feasible, attaining high target S-frequencies requires an initially high S-frequency - much like a raft that can descend but not ascend a waterfall. As Newborn size increases, the region of achievable target frequency is reduced until no frequency is achievable. In contrast, the number of collectives under selection plays a less critical role. In scenarios involving more than two populations, the evolutionary trajectory must navigate entirely away from the metaphorical 'waterfall drop.' Our findings illustrate that the strength of intra-collective evolution is frequency-dependent, with implications in experimental planning.