Evolutionary Feedback Mediated through Population Density, Illustrated with Viruses in Chemostats

Abstract

A cornerstone of evolutionary ecology is that population density affects adaptation: r and K selection is the obvious example. The reverse is also appreciated: adaptation impacts population density. Yet, empirically demonstrating a direct connection between population density and adaptation is challenging. Here, we address both evolution and ecology of population density in models of viral (bacteriophage) chemostats. Chemostats supply nutrients for host cell growth, and the hosts are prey for viral reproduction. Two different chemostat designs have profoundly different consequences for viral evolution. If host and virus are confined to the same chamber, as in a predator-prey system, viral regulation of hosts feeds back to maintain low viral density (measured as infections per cell). Viral adaptation impacts host density but has a small effect on equilibrium viral density. More interesting are chemostats that supply the viral population with hosts from a virus-free refuge. Here, a type of evolutionary succession operates: adaptation at low viral density leads to higher density, but high density then favors competitive ability. Experiments support these models with both phenotypic and molecular data. Parallels to these designs exist in many natural systems, so these experimental systems may yield insights to the evolution and regulation of natural populations.

Viral and microbial community dynamics in four aquatic environments

“…This was observed by the fine-grained recA analyses showing rapid change at the level of microbial strains. These conclusions are consistent with many other studies (Middelboe, 2000;Middelboe et al, 2001;Zhong et al, 2002;Bull et al, 2006;Holmfeldt et al, 2007;Stoddard et al, 2007). Our conclusions are also supported by a recent study linking phage predation to the persistence of microbial diversity at the strain level .…”

“…Likewise, recA-based TaxiF analysis of the microbiomes showed a corresponding rapid change in the microbial strains present. These results are consistent with previous chemostat studies observing limited numbers of viral and microbial pairs (Bull et al, 2006;Lennon and Martiny, 2008).…”

Bacteriophage Adsorption Rate and Optimal Lysis Time

“…Maximization of m is through optimization of t L . The other approach is derived from comprehensive phage population dynamics in a chemostat culture (Bull 2006;Bull et al 2006). The phage growth rate is found to be m ¼ Às 1 rN ðbe ÀtLðd1mÞ À 1Þ, where s is the free phage death rate, r the adsorption rate, N the host concentration, and d the washout rate of the chemostat (Bull 2006, Equation 2b).…”

“…Nevertheless, it is an interesting and important topic worthy of further study. Using a population dynamics model that is based on chemostat culture condition, Bull (2006;Bull et al 2006) derived the optimal lysis time ast L ¼ e 1 ð1=mÞ, where t L is the lysis time, e the eclipse period, and m the phage growth rate, with the circumflexes indicating values at optimum. However, this relationship can also be derived using phage growth rate expressed as m ¼ lnðbÞ=ðt S 1 t L Þ, where t S is the search time for the bacterial host and b is the burst size, which can be expressed as b ¼ m(t L À e), where m is the maturation rate.…”

Fixation Probabilities When Generation Times Are Variable: The Burst–Death Model

“…In contrast, the fixation probability does approach one in the burst-death model when the burst rate, l, is increased and s is very large. Recent work by Bull et al (2006) has elucidated the dynamics of adaptation when changes in both burst size and lysis time are possible.…”