How host-microbiome/holobiont evolution depends on whether the microbiome affects host lifespan or fecundity

There is overwhelming evidence that the microbiome can be important to host physiology and fitness. As such, there is interest in and some theoretical work on understanding when hosts and microbiomes (co)evolve so that microbes benefit hosts and hosts favour beneficial microbes. However, the outcome of evolution likely depends on how microbes benefit hosts. Here, we use adaptive dynamics to investigate how host and symbiont evolution depend on whether symbionts increase host lifespan or host reproduction in a simple model of host and symbiont dynamics. In addition, we investigate 2 ways hosts release (and transmit) symbionts: by releasing symbionts steadily during their lifetime or by releasing them at reproduction, potentially increasing symbionts' chances of infecting the host's offspring. The former is strict horizontal transmission, whereas the latter is also a form of indirect or "pseudovertical" transmission. Our first key result is that the evolution of symbionts that benefit host fecundity requires pseudovertical transmission, while the evolution of symbionts that benefit host lifespan does not. Furthermore, our second key result is that when investing in host benefits is costly to the free-living symbiont stage, intermediate levels of pseudovertical transmission are needed for selection to favour beneficial symbionts. This is true regardless of fitness effects because release at reproduction increases the free-living symbiont population, which increases competition for hosts. Consequently, hosts could evolve away from traits that favour beneficial symbionts. Generally, our work emphasizes the importance of different forms of vertical transmission and fitness benefits in host, microbiome, and holobiont evolution as highlighted by our prediction that the evolution of fecundity-increasing symbionts requires parent-to-offspring transmission.