## Reconsidering the relationship between virally induced bacterial mortality and frequency of infected cells

### Brian Binder*

Department of Marine Sciences, University of Georgia, Athens, Georgia 30602-3636, USA

ABSTRACT: The relative contribution of viral lysis to overall mortality in aquatic bacterial populations is often estimated as twice the frequency of infected cells (FIC). The 'factor-of-two rule' upon which this estimate is based assumes (1) steady-state
conditions, (2) that latent period is equivalent to generation time, and (3) that infected cells are not grazed. FIC values for this calculation are themselves derived from measurements of the frequency of *visibly* infected cells (FVIC) by the use
of a simple conversion factor. A steady-state model was developed to more rigorously define the relationships between FIC, FVIC, and the fraction of mortality from viral lysis (FMVL). This model shows that even under the restrictive assumptions listed
above, the factor-of-two rule systematically overestimates FMVL for typically reported values of FVIC. The model also shows that although grazing on infected cells further reduces FMVL for a given estimate of FIC, at the same time such grazing increases
FIC for a given measurement of FVIC. In combination, these 2 effects minimize the influence of grazing on the calculation of FMVL from FVIC. Overall, the relationship between FMVL and FVIC is well approximated as follows: FMVL ~= FVIC/[
γ ln(2) (1 - ε - FVIC)], where γ = the ratio between the latent period and generation time, and ε = the fraction of the latent period during which viral
particles are not yet visible. Using typically observed values of FVIC, and assuming that γ = 1 (per assumption 2, above) and ε = 0.186 (per literature estimates), the model suggests that, on average,
viral lysis accounts for approximately 22% (range: 4.5 to 45%) of total bacterial mortality in a range of aquatic environments, corresponding to a mean overestimate of 24% (range: 4 to 44%) by the factor-of-two rule. Perhaps most importantly, the model
shows that calculations of FMVL from FIC or FVIC are very sensitive to changes in the relative length of the latent period (γ) and in the assumed proportion of the latent period during which viral particles are not recognizable
(ε). Constraining these 2 factors would greatly improve the reliability of FMVL calculations.

KEY WORDS: Aquatic bacteria · Grazing · Model · Mortality · Phage · Virus