A novel relationship for the maximum specific growth rate of a microbial guild

One of the major parameters that characterizes the kinetics of microbial processes is the maximum specific growth rate. The maximum specific growth rate for a single microorganism (${\mu _{max}}$) is fairly constant. However, a certain microbial process is typically catalyzed by a group of microorganisms (guild) that have various ${\mu _{max}}$ values. In many occasions, it is not feasible to breakdown a guild into its constituent microorganisms. Therefore, it is a common practice to assume a constant maximum specific growth rate for the guild ($\acute{\mu}_{max}$) and determine its value by fitting experimental data. This assumption is valid for natural environments, where microbial guilds are stabilized and dominated by microorganisms that grow optimally in those environments' conditions. However, a change in an environment's conditions will trigger a community shift by favoring some of the microorganisms. This shift leads to a variable ${\acute{\mu}_{max}}$ as long as substrate availability is significantly higher than substrate affinity constant. In this work, it is illustrated that the assumption of constant ${\acute{\mu}_{max}}$ may underestimate or overestimate microbial growth. To circumvent this, a novel relationship that characterizes changes in ${\acute{\mu}_{max}}$ under abundant nutrient availability is proposed. The proposed relationship is evaluated for various random microbial guilds in batch experiments.