Rafting a waterfall: Artificial selection for collective composition can succeed or fail depending on the initial and target values

Collectives, such as microbial communities, can perform functions beyond the capability of individual members. Enhancing these collective functions through artificial selection, however, presents significant challenges. Here, we explore the rafting-a-waterfall phenomenon, a metaphor illustrating how the success in achieving a target population composition in microbial collectives depends on both the target characteristics and initial conditions. Specifically, collectives comprising fast-growing (F) and slow-growing (S) individuals were grown for a period of "maturation" time, and the collective with S-frequency closest to the target value is chosen to "reproduce" (inoculate) offspring collectives. Such collective selection is dictated by two opposing forces: 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. Due to this model structure, maintaining a target frequency requires the continued action of inter-collective selection. 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 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. The range of attainable target frequencies depends on the initial population size of the collectives: as the population size in Newborn collectives 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.