For natural selection to operate there must exist heritable variation among individuals that affects their survival and reproduction. Among free-living microbes, where differences in growth rates largely define selection intensities, competitive exclusion is common. However, among surface attached communities, these dynamics become less predictable. If extreme circumstances were to dictate that a surface population is immortal and all offspring must emigrate, the offspring would be unable to contribute to the composition of the population. Meanwhile, the immortals, regardless of reproductive capacity, would remain unchanged in relative abundance. The normal cycle of birth, death, and competitive exclusion would be broken. We tested whether conditions required to set up this idealized scenario can be approximated in a microbial biofilm. Using two differentially-reproducing strains of Shewanella oneidensis grown on an anode as the sole terminal electron acceptor - a system in which metabolism is obligately tied to surface attachment - we found that selection against a slow-growing competitor is drastically reduced. This work furthers understanding of natural selection dynamics in sessile microbial communities, and provides a framework for designing stable microbial communities for industrial and experimental applications.